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When are Savings Account Balances Highest and Lowest?

Personal Finance      by

In this post, we’ll look at savings account balance by week in the United States. We examine which weeks balances are highest and lowest, and model savings and spending in the United States.

When are Savings Account Balances Lowest?

The lowest balance week in our dataset was the first week of the year in January, followed by the next three weeks sequentially.

The second most common cluster of lowest balance weeks was the 52nd and “53rd” week of the year (around Christmas).

When are Savings Account Balances Highest?

The highest balance week in our dataset was the 52nd week of the year (Christmas). The 49th, 50th, and 51st week of the year were also common.

Interestingly, the 45th week also snuck in. That maps to around October-November.

Keep an Eye on Your Savings Account

Businessman exposing empty pockets showing low savings
The lowest average savings account balances are around New Year’s and Christmas.

First let’s talk caveats.

This is very noisy data due to how dates interact with years and our methodology. Additionally, it doesn’t adjust for inflation (which would make a significant difference some years).

Furthermore, we’re looking at savings and money market balances. It’s possible people transfer money to investments or checking accounts (or otherwise don’t spend money.)

For fun though, let’s continue.

Throw out the years where the first and last weeks mapped to the lowest and highest average savings balance, respectively. If you do that, low balances do tend to line up with Thanksgiving, Black Friday, and Christmas.

Surprising? Probably not – but even this quick study hints at the effect of the end of year purchasing season.

Methodology for Weekly Savings Account Balances

We used an interpolated Civilian Noninstitutional population from FRED and mashed it up with total savings by week. Our dataset extends from 1975 through July, 2019.

Total savings by week is reported on Mondays, so we normalized with the Excel NUMWEEK function (the week number in the year, starting with January 1). Then we looked at relative balances per year to arrive at the statistics you see.

Annual Highest and Lowest Week for Savings Account Balance

How to read this table:

  • Year: Year for savings account observation
  • Week Minimum Occurred: The week of the year we saw the minimum average savings account balance
  • Week Maximum Occurred: The week of the year we saw the maximum average savings account balance
YearWeek Minimum OccurredWeek Maximum Occurred
1975252
1976252
1977149
19785222
1979521
19801945
1981491
19823152
1983128
1984913
1985152
1986152
19875218
19885327
1989221
1990140
1991152
1992151
19931750
1994538
1995161
1996152
1997352
1998352
1999245
2000353
2001451
2002151
2003149
2004150
20052343
20062252
2007534
2008439
2009150
2010250
2011252
2012151
2013445
2014649
2015250
2016252
2017151
2018334

Shout-out to our long time reader Clint for the interesting article idea.

Any thoughts on the noisy data? Think it’s enough to be useful?

American Depositary Receipt Calculator: Model an ADR Investment’s Value

Investing      by

On this page is a American Depositary Receipt return calculator which automatically models reinvested dividends. Enter starting investment and dates to estimate the growth of an investment into an ADR. Also, model periodic investments by year, month, week, or day.

There are over 350 American Depositary Receipt in our database, updated per ticker in the last 7 trading days (see methodology below).

American Depositary Receipt Total Return Calculator with Periodic Investment

How To Use the ADR Return Calculator

To begin, enter at minimum an American Depositary Receipt ticker. As you type, it will auto-complete active ADRs in the DQYDJ database.

American Depositary Receipt return calculator investment entry.
American Depositary Receipt return calculator entry options

Basic American Depositary Receipt Details and Inputs

  • ADR Ticker: Enter IEX valid, active ADR ticker
  • Starting Amount ($): The initial investment amount in the ADR
  • Starting Date: Enter when the investment was initiated °
  • Ending Date: Enter when the investment was sold °

° Depending on the ADR data (see below), we move the start and end date. Check post-calculation.

Advanced Dividend and Periodic Investment Options

Model options for estimating periodic investments and dividend events.
Advanced options concentrating on ADR dividends and periodic investments

Click the ‘Toggle Advanced’ button as shown and we’ll open the advanced ADR investment panel.

  • Show Events: This will list dividend events for the ADR and also optionally include any periodic investment information.
  • Periodic Investments: This will model periodic investments in an American Depositary Receipt.
  • “Monthly”: Select a timeframe in the menu if you want to model periodic investments.
  • Regular Amount: For the selected period the amount to model as a recurring investment.

ADR Model Result Interpretation

  • Final Value ($): The value of the ADR investment on the ‘Ending Date’. (Note again we may change that date depending on our data.)
  • Annual Return: Our estimate of the annual percentage return by the investment, including periodic investments. (Also try our compound annual growth calculator)
  • Graph: The value of the CEF investment over time. On a desktop or laptop, you can hover over a point to see the investment value on any day.
ADR investment Calculator model of an investment in BABA, the Alibaba Group.
ADR Return Calculator result for BABA

How does the ADR investment model work?

In DQYDJ’s database we have 350+ ADR tickers with open, high, low, and closing prices. For many ADRs, we have 15+ years of data in the database.

Your intial sum – and any recurring investments or dividend reinvestments – go in at the open price on a day. Any sales happen on the closing price for the day. The final sale is at the day’s closing price.

On the backend, we maintain a database of all 500+ ADR tickers with open, high, low, and closing prices. For funds which have been around that long, we have at least 15 years of data. (Some have longer.)

What is an American Depositary Receipt?

American Depositary Receipts or ADRs are certificates issued by U.S. bank which represent one or more shares in a foreign company’s stock. ADRs have a fixed exchange ratio with the issuing company’s home country shares, and can either be listed on an exchange or be traded over the counter (OTC).

If you’re interested in investing in ADRs, listed ADRs trade and settle in the same way as stock. They’re a level of abstraction that frees you from dealing with foreign exchange issues, taxation complexities, and securities law compliance in the company’s home country.

ADRs do not perfectly match the returns on shares in the company’s headquarter country. This calculator will estimate returns on ADRs but not on the shares they represent.

Source and Methodology for the American Depositary Receipt Total Return Calculator

The ADR return calculator shares a framework with the stock return calculator and the others. The dividend data should be close to accurate, although we can’t guarantee any data. (Read that again, we can’t guarantee the prices or dividend data although we strive for accurate data).

The IEX Cloud API is how we retrieve price and dividend data. IEX isn’t free.

Since this is a paid service we have (very mild) limits in place:

  • ADR data can be up to 7 trading days old.
    • Check the tool ending date after a scenario, we adjust your scenario to the last updated date.
  • Splits are manual
    • I (PK) have to do splits manually, for now. Please be patient, there are a lot of moving parts.
  • Rectifying Price and Dividend Differences is tough
    • The tool sends me emails when the dividend or price differs between our DB and the API.
  • There are rate limits in place (they apply to the stock, ETF, and CEF calculator in aggregate):
    • Max 50 calculations per day
    • Max 10 calculations per minute

Limitations and Disclaimers

The American Depositary Receipt total return calculator is idealized. It’s based on exact closing and opening prices – no real investor matches the results perfectly.

The tool is for informational purposes only. There is absolutely no warranty on results.

Verify any information you receive from the ADR return calculator independently in your own research. Security price is not the only factor in investment returns.

Here’s a short list of ignore factors:

  • Taxes
  • Dividend timing
  • Portfolio management fees
  • Slippage
  • A zillion things

We also can’t rule out the dividend and price data being wrong, or out of date (in the case of backdating splits). Always check the math.

How to Help with the ADR Total Return Calculator

Let us know if you find a bug. Also tell us the ticker that broke please.

The bar is very high for enhancements. We only make money on this tool through ads. For big requests, make a contracting inquiry.

This tool’s information is for informational and research purposes only. We can’t help you in a legal capacity. We can only help you with research inquiries.

This data is only a useful starting point for legal research. Find a “forensic accountant” if you have legal needs.

American Depositary Receipts, Dividends, Distributions, and Total Returns

We’ve now created four return calculators using the IEX API. Here’s the other three:

Hopefully you’re finding them useful!

As with the others, remember: dividends matter. The return quotes you see on many sites are incomplete; even if you don’t reinvest the dividends you receive from investing they’re worth something.

Want to to compare your results from the ADR return tool to other benchmarks? Here’s some suggested calculators:

You can see all our investment calculators here.

Enjoy the ADR total return calculator, and tell your friends!

Dollar Cost vs. Lump Sum Investing: What to Do with a Windfall

Investing      by

Dollar Cost Averaging (DCA) is oft-touted as the savior for all of investing’s problems. Reality, on the other hand, is a bit different – in this post we’ll show why lump sum investing usually beats dollar cost averaging when you have both options.

We’ll use the S&P 500 in the United States as an example. (Skip ahead if you want to see math the typical difference between lump sum and dollar cost averaging.)

What is dollar cost averaging?

Dollar Cost Averaging (or DCA) is a style of investing where you automatically invest money on a regular interval. You buy more shares when prices are low, and fewer shares when prices are high. In essence, you bet on the average – hopefully DCA prevents you from terrible purchase times.

As a bonus, dollar cost averaging fits the general schedule of how people normally get paid. For example every two weeks you might get your paycheck, and also automatically invest in your 401(k). This is our suggested style of investing on a regular basis.

What is lump sum investing?

Lump sum investing is a style of investing where you have a large amount of money and you invest it all at once. Unlike dollar cost averaging, you don’t slowly wade into the market… you make a big splash.

Lump sum investing is generally not applicable to your paycheck, whether it’s weekly, bi-monthly, or some other regular schedule. It’s more applicable to a windfall, which might include:

  • Annual bonus
  • Sale of equity (that you want to redeploy)
  • Inheritance
  • Tax return
  • Sale of a house
  • Sale of a business
  • Any other one-off, non-repeatable money you receive

When is dollar cost averaging or lump sum investing better?

Dollar cost averaging is on average inferior to lump sum investing... when both options are available. That means if you have a large sum of money to invest, it’s better to invest immediately than to slowly drip it into investments.

Usually, these large sums are called windfalls: large influxes of money you are prepared to invest. They might be from something in that above list or some other source. Whichever way, you now have a large amount of cash you’d like to invest.

When you have extra funds, you usually shouldn’t tiptoe into the market. Instead, you should dive right in with a lump sum investment. 

Don’t believe me? The rest of the post will show you the math.

Lump Sum Investment Caveats

Mathematically, lump sum investing wins more than it loses… but sometimes it’s more important to hedge the risk of a fall than to maximize your expected value.

But if you’re younger, have more risk tolerance, or otherwise have a long time horizon – this tilts the game even more in lump sum’s favor. Still: your situation may be similar, but remember you are unique. 

Always consult a financial planner if you have doubts about implementing any investment strategy. This is not advice, and of course, past performance does not guarantee future results. 

Calculating The Real Return on the S&P 500

We’re using the S&P 500 index, a basket of 500 domestic stocks, as a representation of the total stock market in America. There are other options, but it is a commonly used proxy for the ‘market’ in the United States.

S&P 500 Total Return vs. Index Price Return to illustrate dollar cost averaging and reinvesting
S&P 500 Total Return vs. Index Price Return (1988-2019) S&P Dow Jones Indices

Above you can see a chart of the real price (in orange) that the S&P 500 closed at on the dates listed on the x-axis. The chart covers the period from mid-1989 to mid-2019. 

In blue is the total return price, a made up value which includes the effects of dividends paid and reinvested. This reflects the (estimated) real return of the index, if you held the component stocks and reinvested dividends. 

Using our S&P 500 total return calculator, you can see during the period from June 1988 – July 2019 the S&P 500 returned around 8% index level, and over 10% with dividends reinvested. The gap seems small, but that’s the difference between 1000% and 2000% returns in that time-frame!

So, as you can see we need to take dividend reinvestment into consideration in this math.

Stock Return Drift Rate

It’s true – past performance is no guarantee of future results. However, history does suggest that American stocks tend to increase. Your results may vary… for example look at recent history in Japan.

We like to call the bias for stock to move up and to the right the drift rate.

What is drift rate?

Drift rate or drift velocity is a borrowed term from physics and refers to the average velocity of charged particles – often electrons – in an electric field.

Electrons actually move in all directions, but when you have potential (voltage), electrons tend to move in the same direction. We look at stocks (or at least indexes) the same way: even though they move in all directions on a day, they tend to move up and to the right over time.

What is the daily drift rate of stocks?

On any average day since January 1871, US stocks have increased about .0239%. (Including non-market days and weekends, ignoring inflation adjustments)

Here’s how we get that number:

  • Use the S&P 500 Calculator from January 1871 to July 2019
  • Grab the “Total S&P 500 Return” number: around 41,150,450% total return
  • Calculate the number of days for 148.5 years: about 54,210 days
  • Figure out the drift rate is ~ .0239% a day ( or ~9.09% a year)

Again, historic performance doesn’t guarantee anything about the future. But: there has hitorically been minor upward pressure on US stock in aggregate.

Call it around .02-.025% daily.

Comparing Dollar Cost Averaging and Lump Sum Investing

Now that we have all the ingredients, let’s finally put dollar cost averaging and lump sum investing head to head.

We’ll assume a windfall of $10,000, and either invest it on the first day of the year or invest $192.31 every 7 days:

Lump Sum vs. Dollar Cost Average in a smoothed scenario on the historic S&P 500.
Smoothed DCA vs. Lump Sum investments of $10,000 over one year versus historic S&P 500

And there you have it – at historical average S&P 500 performance and weekly DCA, the dollar cost averaging strategy is $451.25 less after a year. That’s essentially an annual insurance cost of 4.14% off the total potential.

Choosing the Right Investment Strategy

Obviously, this isn’t a perfect simulation. Off our heads, it’s missing:

  • Inflation
  • Interest on the DCA money held in cash while waiting to invest
  • Taxes
  • A lot more…

However, you can see that the normal drift rate of stock means lump sum investing is better when you have the option.

Dollar cost averaging matches well with your paycheck. For deploying a windfall, though, it will typically look like very expensive insurance.

That doesn’t mean it’s not worth it!

Perhaps you can sense – or are very fearful – the stock market will drop in the near future. Maybe it’s psychologically easier for you to drip funds into investments than to throw everything in at once.

And sometimes in retrospect, DCA will come out on top when both options were available. However, the burden is on dollar cost averaging to prove it; the historical default – at least in the United States and most major economies – should be to prefer lump sum investments.

For more details in the real world, you can use our historical investment calculator on the S&P 500.

Enter a monthly average or set a large up-front value for an investment. You’ll see that for a majority of time-frames, lump sum is better… but you can certainly find exceptions.

Takeaway: Lump Sum Usually Beats Dollar cost Averaging

Unless you have good reasons to believe there will be a market fall, or DCA is the only way for you to invest due to psychology… you should bias towards lump sum investing.

Have fun out there, and no matter which style you choose may your portfolio value always move up and to the right!

Inflation and Dividend Adjusted S&P 500 On July 19, 2019

Personal Finance      by

I won’t bury the lede: the all time closing high on the S&P 500, adjusted for inflation and reinvested dividends, was on July 15, 2019.

Friday’s close (July 19, 2019) was a mere 1.23% below that peak .

The S&P 500 Through July 2019

After Christmas Eve 2018 we talked about how the S&P 500 – intraday – dipped to the definition of a bear market. It temporarily dropped 20% below its nominal all time high.

We’ve since completely erased that bear, even with the currently looming economic issues here in the US (for starters, a Federal Reserve about to cut rates and an inverted yield curve).

That lull now looks like a pothole in an otherwise stereotypical up and to the right graph 📈:

Inflation and dividend adjusted S&P 500 from January 2015 - July 2019.
Inflation & dividend adjusted S&P 500 from January 2015 – July 2019

(Above, blue is the adjusted “index” level and orange is the un-adjusted.)

In fact, by this math we left the bear market on April 19, 2019. The journey hasn’t been entirely smooth since that time – note the volatility increase you can actually see. We can say one thing for certain though: the brief bear market did not affect the general trend of the market.

But you already know that part. I just wanted to show you that we’re at an all time high even adjusted for dividends and inflation.

Floating Near an All Time S&P 500 High

So, even with a bit of weakness last week we’re still sitting near an ATH.

Why bother doing this math?

Frustratingly, even in 2019, the most commonly watched investing numbers revolve around index levels. As you know, dear reader, you don’t (only) make or lose money off the level of an index.

There are two major oft-ignored investment factors:

  • Dividends: what stocks pay out doesn’t show up in index levels, but does show up in your wallet
  • Inflation: even if the value of your investments are increasing, it doesn’t help if the prices of things you buy are increasing faster

(Okay, taxes too – but with worldwide readership on DQYDJ plus all of the various retirement accounts that’s a hairy one)

Anyway, that’s why we do this math – it’s more informative to look at investment results factoring in real world factors like dividends and inflation.

For the newer readers, over the years we’ve built a number of calculators with this philosophy in mind:

And what are you going to do about US stocks?

Earlier this year we laid out our current asset allocation. I told you then we were targeting around 60/40 risky/safe assets. We’re in our mid-thirties, so that’s a conservative allocation.

The stock market success and company equity vest have pushed us past 70/30. I’m looking at trimming it a bit and pocketing 2%+ money market and safe fund returns for now. 2% returns are presumably temporary with the Fed rate cut on the horizon, so hold me to investing hard if we do see weakness.

It’s going to be an interesting next 12 months! In the comments, let us know how you’re approaching the current market.

Bond Yield to Worst Calculator (YTW)

Investing      by

On this page is a bond yield to worst calculator. Depending on the characteristics of a bond and its current market price, it computes the yield to worst – the worst yield you could see between any call features or maturity (but see the note below).

Yield to worst is the lower of yield to maturity or yield to call.

Importantly, it assumes that all payments are made on time and the issuer doesn’t default.

Bond Yield to Worst Calculator

Yield to Worst Calculator Inputs

  • Current Bond Trading Price ($) – Today’s trading price on the bond.
  • Bond Face Value/Par Value ($) – The face value (“par value”) of the bond.
  • Years to Maturity – The numbers of years until the bond matures.
  • Annual Coupon Rate (%) – Annual percentage paid on the face value of the bond.
  • Coupon Payment Frequency – How often the bond makes coupon payments.
  • Is the Bond Callable? – “Is the bond in question callable?”. Essentially, does the bond have a prepayment or early redemption feature.
  • (If callable) Price to Call ($) – Generally, callable bonds have some premium if they choose to exercise the option (more than the par value). Enter that here, or enter the bond face value if it doesn’t exist.
  • (If callable) Years to Call – How long from the current date is the first opportunity for the bond to be called.

Bond YTW Calculator Outputs

  • Yield to Worst (%) – The lowest ongoing yield you’ll earn between either yield to maturity or yield to call.
  • Worst comes from – Either yield to maturity or yield to call depending on which is a lower yield

What is Bond Yield to Worst?

Ladder with one step broken denoting the worst that can happen
Always assume the worst yield when investing in a bond.

Bond yield to worst is a hybrid measure of yield to maturity or yield to call. YTW is the lowest of yield to maturity or yield to call assuming the issuer doesn’t default.

To compute yield to worst manually, calculate yield in both ways including yield to call assuming the bond is called when that option becomes available. Or, make it a bit easier on yourself and use our calculators:

Note once again: Even though ‘worst’ is in the phrase, YTW assumes all payments are on schedule and the issuer doesn’t default. (A default is – presumably – the actual worst case.)

Why Use Yield to Worst?

Yield to Worst is an investor-focused measure: it answers what’s the lowest yield you might see on your bond investment. That is, again – assuming the issuer doesn’t default.

Assuming the issuer is perfectly rational and there are no other extenuating circumstances, you can make some behavioral assumptions based on the yields.

A rational issuer will either call a bond if it makes sense financially or otherwise let a bond mature normally. That model doesn’t necessarily hold up in the real world, but it’s a reasonable view when evaluating your investment options.

You should always calculate yield to worst on any bonds you consider for investment. If your bond isn’t callable (and the issuer doesn’t default!), you’ll pick up the yield to maturity for the entire time-frame. And if it is callable, you’ll want to calculate yield both ways and assume you’ll capture the lower of the two yields.

If you beat yield to worst while actually investing? Congrats…

…but please base your assumptions on the more pessimistic number.

Financial Basics and Bond Valuation Calculators

Use the Yield to Worst in place of either Yield to Call or Yield to Maturity – even if it doesn’t play out, it’s best to assume the worst. Being overly conservative with your bond modeling means you can only be pleasantly surprised.

Always beware the overall risk of the bond, but keep yield to worst in mind when investing.

If you’re interested in the topic, Wikipedia also gives a decent overview of bond valuation.

Yield to Worst on a Bond

For other calculators in our financial basics series, please see:

Bond Yield to Call (YTC) Calculator

Investing      by

On this page is a bond yield to call calculator. It automatically calculates the internal rate of return (IRR) earned on a callable bond assuming it’s called at the first possible time. Importantly, it assumes all payments and coupons are on time (no defaults).

Also, find the approximate yield to call formula below. Like with Yield to Maturity (YTM), Yield to Call is an iterative calculation. There is a shortcut equation to guess a yield to call which we cover below.

Bond Yield to Call Calculator

Yield to Call Calculator Inputs

  • Current Bond Trading Price ($) – The trading price of the bond today.
  • Bond Face Value/Par Value ($) – The face value of the bond, also known as par value.
  • Price to Call ($) – Generally, callable bonds can only be called at some premium to par value. If there is a premium, enter the price to call the bond in this field.
  • Years to Call – The numbers of years until the bond can be called.
  • Annual Coupon Rate (%) – The annual percentage paid on the bond based on the par value (read: do not recompute it for the current trading price, the tool will handle it.)
  • Coupon Payment Frequency – How often the bond makes coupon payments.

Bond YTC Calculator Outputs

  • Yield to Call (%): The converged upon solution for the yield to the call of the current bond (the internal rate of return assuming the bond is called).
  • Current Yield (%): The simple calculated yield which uses the current trading price and face value of the bond.

Bond Yield to Call Formula

The calculation for Yield to Call is very similar to Yield to Maturity.

When making this calculation, we assume the bond will be called away at the first opportunity. Additionally, the price to call bond is usually a bit more than the face value of the bond – we use the price to call for this formula instead of the par value in YTM.

Estimated Yield to Call Formula

However, that doesn’t mean we can’t estimate and come close. The formula for the approximate yield to call on a bond is:

( (Annual Interest Payment) + ( (Price to Call – Current Price) / (Years to Call) ) )

/

( ( Price to Call + Current Price ) / 2 )

Estimating Price to Call for the Calculator Scenario

Let’s solve the default entry of the calculator:

  • Current Price: $920
  • Par Value: $1000
  • Price to Call: $1050
  • Years to Call: 5
  • Annual Coupon Rate: 10%
  • Coupon Frequency: 2x a Year

100 + ( ( 1050 – 920 ) / 5)

/

( 1050 + 920 ) / 2

=

100 + 26

/

985

=

12.792%

Exact Yield to Call Formula

Of course, if you hit the ‘Calculate’ button you get a different answer – namely, you’ll get 12.966%. Why the disparity?

Internal to the tool, we calculate the return an investor would see then look at the present value of those cash flows.  The summation looks like this:

Price =

Coupon Payment / ( 1 + rate) ^ 1

+

Coupon Payment / ( 1 + rate) ^ 2

…

+

Last Pre-Call Coupon Payment + Cost to Call / ( 1 + rate) ^ n

The calculator internally uses the secant method to converge upon a solution, and uses an adaptation of a method from Github user ndongo. The discussion of the formula itself is a bit heavy, but start with our references in the Yield to Maturity Calculator to read more.

(Yes, you’ll want to do the math with a computer. Which… is what this site is, I suppose.)

Yield to call calculator screenshot showing approximate yield on a bond callable in 5 years.
Presumably, the issuer would not call this bond away.

Why Does Yield to Call Matter?

When you start investing in bonds, you’ll soon recognize that bonds can either be callable (“redeemable”) or un-callable. Callable bonds usually offer some sort of perk – like a higher interest rate – with the risk that the issuer might call it before its full maturity. If you don’t care about the duration, it can be a win-win – a slight edge in yield, while the issuer can hedge a bit against falling interest rates.

In a sense, callable bonds are very similar to some forms of consumer debt.

Take mortgages, for example. When mortgage rates fall, people rush to refinance their current mortgages. In a refinance, people prepay – “call” – their current mortgage, paying it off in full. They then effectively reissue a bond at the prevailing rate… only to restart the cycle if rates fall an acceptable amount in the future.

It’s not a perfect comparison, sure. (There are usually no prepayment premiums, most cost is up-front on a mortgage, etc.) However, it’s a useful model to keep in mind when investing in bonds.

Know this: callable bonds might not behave exactly as you planned (although we assume the calculator default bond wouldn’t be called!). Computing YTC like we’ve done in the calculator shows you the yield on your bond if it doesn’t make it to maturity.

Conclusion and Other Financial Basics Calculators

Use the Yield to Call as you would use other measures of bond valuation: a factor in your decision whether to buy or avoid a bond.

Yield to Worst on a Bond

Combining Yield to Maturity with Yield to Call and taking the minimum is known as the Yield to Worst. While yield to worst doesn’t show you duration, it does show you the worst (from your perspective) possible annual yield you’d make when considering a bond.

If your bond is called, presumably you’ll have to find another investment to substitute for it.

Yield to worst on a non-callable bond is exactly equal to the yield to maturity. On a callable bond, it is the lower of the yield to maturity and yield to call.

For other calculators in our financial basics series, please see:

Closed End Fund Total Return Calculator: What would your investment be worth?

Personal Finance      by

On this page is a Closed End Fund return calculator which can automatically compute reinvested dividends. Enter a starting amount and investment dates to estimate the growth of a closed end fund investment. Also, model periodic investments in a CEF by year, month, week, or day.

There are over 500 closed end funds in our database, updated per ticker in the last 7 trading days.

Closed End Fund Total Return Calculator with Periodic Investing

How To Use the CEF Return Calculator

To begin, enter at minimum a ticker for a closed end fund. As you type, it will auto-complete active closed end fund tickers in the DQYDJ database.

Closed End Fund return calculator date and initial investment entry.
Closed End Fund return calculator entry options

Basic Closed End Fund Details and Inputs

  • CEF Ticker: Enter a valid, active CEF ticker from IEX
  • Starting Amount ($): In dollars, the initial investment amount
  • Starting Date: Enter a date when an investment was first made °
  • Ending Date: Enter a date when an investment was sold °

° Depending on the CEF data (see more below), we adjust the starting date and ending date. Check after your calculation.

Advanced Dividend and Periodic Investment Options

Model options for estimating periodic investments and dividend events.
Advanced options concentrating on CEF dividends and periodic investments

Click ‘Toggle Advanced’ to open the advanced CEF investment panel.

  • Show Events: Check the box to list dividend events for the CEF. We’ll also optionally include periodic investment information.
  • Periodic Investments: Select the box to model periodic investments in a closed end fund.
  • “Monthly”: To simulate periodic investments, select a timeframe.
  • Regular Amount: The amount invested every period in the closed end fund.

Interpreting CEF Model Results

DNP Closed End Fund performance result from tool
DNP performance in a CEF investment model
  • Final Value ($): The value of the CEF investment on the ‘Ending Date’. (Note again we may change that date depending on our data.)
  • Annual Return: Our estimate of the annual percentage return by the investment, including periodic investments. (Also try our compound annual growth calculator)
  • Graph: The value of the CEF investment over time. On a desktop or laptop, you can hover over a point to see the investment value on any day.

How does the CEF investment model work?

On the backend, we maintain a database of all 500+ CEF tickers with open, high, low, and closing prices. For funds which have been around that long, we have at least 15 years of data. (Some have longer.)

When you choose your dates, we invest the initial lump sum at the open price. We then calculate the portfolio value at the daily close for other days, including the final day in the scenario.

Source and Methodology for the Closed End Fund Total Return Calculator

The CEF return calculator uses the same backend as the stock return calculator. The dividend data should be reasonably accurate, although we can’t guarantee any distribution data – including returns of capital (common for closed end funds).

We use the IEX Cloud API to retrieve price and dividend data. IEX isn’t free. Our tool has some (very mild) limits in place:

  • CEF data may be up to 7 trading days old.
    • Always check the tool ending date after a scenario to see how recently we updated a CEF.
  • Splits are a manual process
    • I personally apply split factors. (I might automate these eventually – for now please be patient)
  • Rectifying Price and Dividend Differences is a manual process
    • If daily price or dividend differs significantly (more than a percent), I’ll update manually. Please be patient.
  • There are rate limits in place across all the tools:
    • Max 50 calculations per day
    • Max 10 calculations per minute

Limitations and Disclaimers

The closed end fund total return calculator uses idealized return data. The math is based on exact closing and opening prices and would never match a real investor’s gains exactly.

The tool is for informational purposes only. We cannot warrant any results. Verify any information you receive from the CEF return calculator independently through your own research.

Security price isn’t the only factor in investment returns. A short list of other things we’re ignoring:

  • Taxes
  • Dividend timing
  • Portfolio management fees
  • Slippage
  • A plethora of other things

It’s also possible – likely even – that the price and dividend data is wrong for some tickers. Again, you need to independently verify any data the tool outputs.

Bug Reports, Feature Requests, and Requests to Help with the CEF Total Return Calculator

Let us know if you find a bug. Include the fund with the issue otherwise I can’t debug it.

Send enhancement requests too, just know that the bar is very high. This tool is only monetized through ads. For significant requests, make a contracting inquiry.

This tool’s information is for informational and research purposes only. We can’t help you in a legal capacity. We can only help you with research inquiries.

This data might be a useful starting point for legal research. You probably need to engage a “forensic accountant” to present data in a manner suitable for legal purposes.

Closed End Funds, Dividends, Distributions, and Total Returns

When we set out to build the stock return calculator a few months ago, we made it modular. Between this calculator, the ADR Return Calculator, and the ETF return calculator, we’re now using the same codebase for three types of securities!

… And stocks and ETFs are likely to remain the popular ones, haha. But for those of you waiting for CEF data, you’re probably pretty excited with this unveiling!

Anyway, the same message we closed on in the other tools applies: dividends matter. Unless you’re shredding your dividend checks, dividends are real money that you need to factor into your investment returns. Even if you aren’t reinvesting dividends, you need to model something with that money.

If you’d like to compare your results from the CEF return tool to other benchmarks, we have… a few. Here’s a limited selection:

You can see the larger collection on our calculator landing page.

We hope you enjoy the CEF total return calculator. Have fun with it, and tell everyone you know!

CAPE, Interest Rates, and Poor Future Returns

Investing      by

Today we’re elated to host this epic guest post from Fat Tailed and Happy, who writes at his eponymous blog. Enjoy!

Robert Shiller received a Nobel Prize for linking long term stock returns and valuation. His work has since been proved in numerous economies over the past two centuries.

Yet, Shiller’s preferred valuation metric, the cyclically adjusted price to earnings ratio (CAPE), explains only about 40% of the deviation in long term returns. This loose correlation frequently leads to critiques from the random-walk community who contend CAPE is of no use in investing around the business cycle.

I’m honored for this opportunity to expand on Shiller’s work.

Using data from 1920-Present, equity returns show a clear dependence on CAPE, interest rates, and time itself. Unfortunately, data suggests the trends which made recent strong equity performance possible are reversing. It is therefore possible that future returns may be poor.

CAPE And Forward Returns

CAPE smooths valuations by using the average earnings of the preceding 10 years in its calculation of valuation. Earnings typically increase during expansions and decrease during recessions; the attraction of CAPE is it accounts for both of these periods with the longer time lag. 

Higher values of CAPE mean stocks cost more for a dollar of earnings than in the past, reflecting an overvalued sentiment. Shiller’s critical finding was that ten-year returns are negatively related to CAPE. The loftier the starting value, the poorer the subsequent return:

10 year subsequent equity returns vs. Shiller CAPE

Despite its power, CAPE is a poor indicator for shorter term allocation and only explains about 40% of stock returns. It is the latter point we seek to improve.

The Importance of Time

Markets of 150 years ago certainly had nowhere near the oversight and regulation of the modern day, nor were the accounting standards or breadth of market exposure comparable. Additionally, tax rates, trade regimes, and a multitude of other factors undoubtedly influence equity valuation – and dramatically.

A fully specified treatment of each of these factors is beyond the scope of this post. However, this DOES suggest equity returns may structurally differ across time.

Therefore, equity return estimates may be improved by including two additional variables to CAPE:

  1. Interest rates on bonds provide clear signals of the appropriate value of time and govern the discount for future earnings. 
  2. Time itself serves as a proxy for legislative complexity.

Modeling

Robert Shiller provides all of his data to the public, and it must hold the record for the most traffic to something that looks like an old Geocities site from 1994. 

Three econometric models of his data follow using data from 1920-Present. In all cases, the annualized real forward ten-year return of stocks is the variable in question. As an example, for the year 2000:

  • We analyze annualized returns from 2000 to 2010, net of inflation
  • Variables used to explain future returns are interest rates, CAPE, and time effects as of 2000

Three specifications follow:

  1. “CAPE ONLY” – Predicts stock returns on the basis of ONLY CAPE
  2. “CAPE, Interest, Time” – Uses CAPE combined with nominal interest rates. Time trends pick up a constant increase in equity returns.
  3. “CAPE, Interest, Decades” – Uses a separate adjustment for each decade, normalized to the 1920s. This permits each decade to have a structurally different tax or trade structure.

Model Results & Catharsis

MARKET RETURNS VS CAPE : 1920 – PRESENT

 CAPE ONLYCAPE, Interest, TimeCAPE, Interest, Decades
R-Squared0.4000.5240.819
Constant0.147 0.110 0.184 
CAPE(0.005)(0.007)(0.007)
Interest Rate–(0.006)(0.005)
Time Trend–0.001 –
1930s––(0.035)
1940s––0.024 
1950s––0.039 
1960s**––(0.017)
1970s**––(0.019)
1980s––0.065 
1990s––0.081 
2000s––0.062 

** Variables Not Significant At 95% Level

CAPE

Increasing CAPE by 10 lowers future real returns by 7% per year over the subsequent decade. CAPE explains about 40% of the variation in equity returns and cannot be ignored.

Interest Rate

A 1% increase in the 10-year yield trims half a percent annually to stock returns. This matches intuition: lower interest rates allow corporations more leverage and cheaper financing, boosting future earnings. 

Impact Of Time

Graph of the outperformance (or underperformance) of US stock unexplained by valuation or rates.

Both time models find a positive relationship between time and equities. Upon closer analysis, real returns found a tailwind in the 1980s which resulted in 6% to 8% MORE annual real returns even after adjusting for CAPE and interest rates. Time evolution and CAPE each explain 40% of future returns.

We conclude CAPE, interest rates, and market structure are critical to future returns. 

Why Are Returns Getting Bigger Over Time?

The increase in equity returns over time, beyond other factors, is curious. What explains this?

Certainly, tax trends over the period have been biased towards more favorable corporate tax policy.

Additionally, the fundamental engine of corporate profits is productivity. Automation, moving supply chains to low cost areas, and improved decision making with technology shows up as lower costs and a healthier bottom line.

The rapid globalization in the aftermath of the Cold War meant US companies could source materials efficiently and cheaply from overseas suppliers while technology meant workers became ever more productive in their roles. Profits and stock prices exploded.

Federal Reserve data to 1980 confirms this. Corporate profits as a share of GDP increased dramatically up until nearly 2010, and then decayed.

Graph of corporate profits post-tax during increasing real output per worker in the United States from the 80s until 2010, and the fall since then.

The same phenomenon persists in worker productivity numbers; worker output grew strongly until the Great Financial Crisis; it has since struggled to improve:

AVERAGE PRODUCTIVITY GROWTH

1980s1.6
1990s2.2
2000s2.8
2010s0.9

Source: Nonfarm Business Sector Real Output per Hour Percentage Change

Uncharted Territory

I believe the trends which explain why stocks outperformed so strongly in 1980-2010 are now reversing, and we see it in the faltering productivity data above. 

Demographics: The 1980s to 2010s coincided with favorable demographics as baby boomers hit their productive stride. Nearly 50% of GDP growth originates from raw population growth, and we now see an aging American workforce with low birthrates and an increasing hostility towards immigration. We’ve already witnessed what this did to GDP in Japan and now Europe. It isn’t good. 

Trade: A significant portion of the country supports protectionism and believes that tariffs to protect American jobs are sound policy. I will not go into the politics of that discussion (though I have looked at Milton Friedman quotations on the topic), but increasing costs in production counter the trends from the preceding 30 years. It is not bullish for stocks.

Economic Growth: In the opposite of recession, there are two clear trends in US expansions: 1) they are longer, but  more sluggish and 2) equity returns correlate to the strength of expansions. A low growth world struggles to sustain higher equity returns. 

Interest Rates: At the zero bound, the impact of interest rates may reverse. While lower rates are good for earnings, they also influence the discount on future earnings and the equity risk premium. What happens with real rates of zero (or lower) in perpetuity? Could future returns already be priced in?

CAPE: In the 150+ years of Shiller data, it is literally unprecedented to see CAPE in the 30s with real rates this low. We are in uncharted territory.

On the basis of these fundamental factors, it seems as though the strong outperformance will be difficult to replicate in the coming decade. 

Expected Returns

As a result, the prognosis for the future isn’t great. In the following chart, black indicates actual returns with corresponding model fits plotted in color. All are based on CAPE.

CAPE Based models including interest and time versus actual subsequent US equity returns.

The time-based models fit the best; return projections suggest a range from very tepid to downright atrocious.

DISCLAIMER: NONE OF THIS IS ACTIONABLE FINANCIAL ADVICE AND IS FOR INFORMATIONAL PURPOSES ONLY.

FORECASTED 10Y RETURNS

CAPE ONLYCAPE. Interest, TimeCAPE, Interest, Decades
2019-20290.008%-0.025% to 3.5%5.900%

The middle result requires some clarification. 

Assuming we achieve the ~6% outperformance achieved since the 1980s, the forecast is 3.5%. Were the fundamental factors identified above to hamper this growth (as I believe they might), real returns might be as low as -0.025%.

This DOES suggest a more bullish potential world than CAPE alone allows (0%). But returns are still far below average. 

Tying It All Together

The above is a lot to digest. 

The key points are:

  • Stock returns undoubtedly depend on CAPE and interest rates. We know what these are.
  • They also depend on time-dependent subtleties of each decade. We know what these were.
  • Evidence suggests it will be hard for the economy to replicate the past because structural currents flow against it.

The totality suggests a difficult environment moving forward for stocks over the next decade, albeit returns will likely be stronger than predicted by CAPE alone. Strong performance will require some mechanism to dramatically lower corporate costs, either by lower labor, freer markets, or technological revolution…… or…. a material correction in prices.

Fat Tailed And Happy holds a PhD in economics and writes about CAPE, recessions (including recession proof businesses), economics, and safe withdrawal rates in a low return world. The preceding analysis is for informational purposes and is not financial advice.

Comments or suggestions greatly welcomed here or on Twitter @FatTailedHappy

Return on Investment (ROI) Calculator

Investing      by

Pile of coins

On this page is a return on investment calculator, often abbreviated ROI.

Enter a beginning and ending amount and time-frame and we’ll compute your return on investment. Also, we’ll calculate your annual return and absolute investment gain or loss.

Return on Investment Calculator

Using the Calculator

ROI Calculator inputs
Inputs to the ROI Calculator
  • Starting Amount – The initial value of the investment
  • Final Amount – The value at the end of the time period
  • Two dates or fixed timeframes? – Enter a range of time by picking a start and end date or entering a number of years
    • (Two Dates) Enter Starting Date and Ending Date
    • (Fixed Timeframes) Enter Number of Years (you can use decimals)
  • CAGR/Return per Period – The percentage gained as a compound annual growth rate or CAGR (‘per period’ normalized growth)
Return on investment calculator outputs after running a scenario
Outputs after running the return on investment calculator
  • Investment Gain – The total earnings or loss on the investment, i.e. the final value minus the starting value
  • Total Return on Investment – The total percentage gain (the true ROI) on the investment over the entire timeframe
  • Compound Annual Growth Rate – The value of the total return when converted to an annual gain or loss

What is Return on Investment?

Return on Investment is one measure of an investment’s profitability. By taking the earnings on an investment and dividing it into the initial outlay, the remaining percentage is the return on investment.

ROI is often quoted as the percentage gain in some investment, or alternatively the total return (measured in dollars or some other currency) net of an initial investment.

How does ROI differ from CAGR – compound annual growth rate?

CAGR or compound annual growth rate is a normalized measure of your investment’s performance. Since money invested in one place is not invested elsewhere, CAGR is a fair way to compare two investments by the rate they return gains quoted as an average gain or loss per year.

CAGR is a useful lens for you to compare investment returns (and why we included both ROI calculations and CAGR in the ROI calculator).

Visit our compound annual growth rate calculator for a longer discussion on CAGR.

Return on Investment Formula

The basic return on investment formula is:

((final value - initial investment) / initial investment) * 100 = ROI

The last step – multiplying by 100 – is just to convert the result into an easy-to-quote percentage.

Annualized ROI

Annualized ROI is effectively the same thing as compound annual growth rate.

Quickly, you can compute your annual percentage return on investment with this formula:

(((final value / initial value) ^ (1/years))-1) * 100 = annualized return on investment

As in the above ROI formula section, the *100 step is just convenience for quoting a percentage. The result is “X% per year” return.

Absolute Return on Investment

Absolute return on investment isn’t much of a formula.

Really – just subtract your initial investment from your final value. That result is the actual return on investment, positive or negative.

final value - initial investment = final return on investment

Even though it isn’t much of a formula, your absolute return is arguably the most important number here. Well – it is according to most governments.

In the United States, you are taxed on your capital gain (or save taxes on a capital loss). Regardless of your percentage ROI, value at risk, time in the market, etc, capital gains taxes apply.

(Capital gains also ignore inflation in most places).

ROI Calculation Example

Let’s walk through all three of the relevant formulas above in a simple ROI calculation example. I’ll draw it out manually, but you should also use the above tool for clarity.

Let’s make the following assumptions:

Initial investment: $1,000
Final value: $3,000
Time in market: 3 years

Let’s compute all of the return on investment numbers we care about.

Absolute Return on Investment

First, let’s look at the absolute return on investment, or “earnings”. (For individual investments in the United States, this is your capital gain or capital loss).

Earnings = $3000 - $1000
Earnings = $2000

Excellent – ignoring time, this investment made you $2,000. Let’s move onto ROI.

Return on Investment

Now, let’s look at the core number for return on investment, or the percentage gain (or loss). From the above formula, (final value - initial investment) simplifies to earnings so we can use the above $2,000 directly in the formula.

ROI = ($2,000 / $1,000) * 100
ROI = 200%

So, you made a 200% ROI – nice work. Now, let’s look at how you performed over time. We’ll use years as the period since it’s the most popular way to compare results.

Annual Return on Investment (Compound Annual Growth Rate)

Now, let’s take that 200% return, or $3,000 in final value on $1,000 investment, and look at the return annually.

CAGR = ((($3,000 / $1,000) ^ (1/3))-1) * 100
CAGR = ((3 ^ (1/3))-1) * 100
CAGR = (1.44224957031-1) * 100
CAGR = 44.225% annual return

Wow, that’s a great investment – you made an average 44.225% annual return in this scenario. That’s much higher than the historical average on the S&P 500, for example.

And there you have it. After working through the parameters for return on investment you now have:

  • Absolute return on investment or capital gains to report on taxes
  • Return on investment percentage to see your total return
  • Annual return on investment or compound annual growth rate to compare to other investments

Other Financial Calculators

To drink from the DQYDJ calculator firehose, try all our finance calculators. If you’re in the mood for similar content, see these other tools in our financial basics series:

Inflation Expectations in June, 2019

Personal Finance      by

Don’t look now – inflation expectations are getting interesting again.

Last year, inflation expectations as measured by the difference between inflation adjusted securities – TIPS – and nominal treasuries floated around 2-2.15% for 5-30 years. As of today, those time-frames predict 1.61% annually over the next 5 years and only up to 1.81% over the next 30.

(Somewhat) Closely Monitoring Inflation Expectations

Previously, we used to check in on inflation expectations once a month here on DQYDJ.

Frankly… it got a bit boring.

The Federal Reserve and/or other actors in the economy convinced investors that the economy was on track for targeted 2% inflation. You can only write about well behaved indicators for so long.

For essentially all of 2018 – and really dating back to mid-2016 – inflation expectations on the 5-year breakeven were closer to the 2% target than they are today.

Inflation expectations between January 2018 and June 2019
Inflation expectations from the beginning of 2018 until today.

Outside of a few dips in 2017 and the swoon in October-November, we’re now challenging the lowest expectations we’ve seen under President Trump.

DATE5 YR Expectations10 YR Expectations20 YR Expectations30 YR Expectations
6/3/191.56%1.73%1.80%1.81%
6/4/191.59%1.74%1.83%1.83%
6/5/191.59%1.75%1.84%1.85%
6/6/191.58%1.73%1.82%1.82%
6/7/191.61%1.74%1.80%1.81%

To read these: X% a year over the next Y years.

Since 5 year TIPS are the most volatile in the series, here’s a chart looking at their performance over the last 20 years:

So, everything has fallen – real and nominal.

Inverted Yield Curve and Dipping Inflation Expectations

We’ve talked a bit about the inverted yield curve here on the site. As it turns out, the 2 year 10 year still isn’t inverted, while the more important 3 month 10 year remains awkwardly inverted.

(If you’re looking to refinance 3 year to 10 year ARMs are tempting. Also, Bay Area house prices have stalled which is… a thing.)

Throw the behavior of Treasury break-evens (they aren’t the best measure of inflation, but good for a quick measurement) on top? Count your humble host as wary about the economy’s prospects for the rest of 2019.

Convince me otherwise in the comments – how do you see the rest of 2019 playing out?

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