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 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.)
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.
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.
For other calculators in our financial basics series, please see:
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.
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.
However, that doesn't mean we can't estimate and come close. The formula for the approximate yield to call on a bond is:
\frac{(Annual\ Interest)+((Price\ to\ Call-Current\ Price)/(Years\ to\ Call))}{(Price\ to\ Call+Current\ Price ) / 2}Let's solve the default entry of the calculator:
\frac{(100)+((1050-920)/5)}{(1050+920 ) / 2}=\\~\\\frac{100+26}{985}=12.792\%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} +\\ ... + Coupon\ Payment/(1+rate)^{-n}+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.)
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. And it's not always against you – some bonds have a put option; see the yield to put calculator for the nearly-equivalent yield to put.
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.
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:
On this page we examine the history of the relationship between long term and short term government debt yields in the United States. We're especially interested in when the yield curve inverts - or short term borrowing costs exceed longer term costs.
In a recent inflation article, we examined the yield curve measured by the 10 year and 2 year US Treasury. This article pulls the series back to January of 1871 by merging data on various short term debt instruments and comparing them to the 10-Year US Treasury Yield.
10 Year Treasury Yield v. Short Term Debt, 1871 - Today (Click to enlarge)
Pictured above is the 10Y – 3-6 Mo US yield difference from January 1871 through April 30, 2018. Since the yield curve is a curve (ha) we're showing the difference between just two points: short term and long term debt. Those terms are rather ambiguous, and we are about to make it worse:
Any time you toss recessions onto a graph with a decent timeline you recognize the stability after the Federal Reserve came into play (and especially after modern government debt issuance practices). While we speak of 7-10 year business cycles nowadays, recessions used to be quite common in the United States.
Indeed, the whole yield curve inversion omen is a modern-ish invention. The first time it was even usable as a harbinger of recession was when the curve inverted in the midst of World War I in May of 1917 (recession followed ~1.5 years later). Before that it wasn't obvious that long term US government Debt had supremacy over short term debt - or even commercial paper!
Since then it's been a reliable sign of an impending recession - even using the imperfect blended measure we came up with for this post. (Want to explore interactively? Our 3D Treasury Yield Curve Chart visualizes daily yields from 1990 to today — rotate, zoom, and animate through time to see inversions form and resolve.)
However, it isn't an immediate measure. In the next post we'll look at timing with the inversion and what it all means - and clean up the data to release to you folks to do your own work.
Long-term borrowing costs are relatively simple to find. If you read DQYDJ, you know we're big fans of Robert Shiller's work. For the 10 Year Treasury rate, we took his series which extends back to 1871.
On the other hand, unified data on historical short-term US borrowing costs is hard to come by online.
While ideally we would use 2-Year Treasuries as the short-term point, they're a relatively modern invention. In fact, treasury note auctions in general weren't even a thing in the US until 1929. Prior to government bond issuance in the late 1910s, short term commercial paper (!) was the best proxy for short term interest rates (as documented by Lawrence H. Officer of University of Illinois at Chicago in What Was the Interest Rate Then? A Data Study [PDF]).
Long story short, to counter the 10 year on the short-term side we blended four series into one:
Finally, we used the NBER-determined business cycle and recession periods.
Merged series comprising DQYDJ short term US Debt estimates
Visually, you can see that the sets are well-correlated. It's not perfect though, so we took the average difference between the series to come up with estimated adjustments to blend the rates. Our gold standard for 'short-term' was the 3-month Treasury Bill secondary market rate.
The final adjustments, for your consideration:
To translate: these are quick cuts, not graduate thesis-level adjustments to blend these rates. Consider this a decent jumping off point for your own scholarship.
Putting it to work: this same blended short-term series is the cash (and risk-free) benchmark in our Stocks vs Bonds Historical Returns calculator, where you can run it against the S&P 500, the 10-year Treasury, and a 60/40 portfolio back into the 1800s.
This page contains a bond pricing calculator which tells you what a bond should trade at based upon the par value of the bond and current yields available in the market (sometimes known as a yield to price calculator).
It sums the present value of the bond's future cash flows to provide price. It returns a clean price and dirty price (market price).
Accumulated interest on a bond is easy to calculate. The only trick is a shortcut due to the day count convention; we assume here a round number of days for the various periods which don't exactly match the calendar. If the slight error doesn't match the payments on your bond, we suggest you calculate them on your own using our guidelines but substituting for your inputs.
Anyway, this is what we are using for 'the time between payments' internally to the bond pricing calculator:
The accrued interest formula is:
F * (r/(PY)) * (E/TP)
Where:
Using the example in the calculator, but with 45 days elapsed:
1000 * (.1/2) * (45/180) = $12.50
As in our yield to maturity calculator, this is a hard problem to do by hand. The trading price of a bond should reflect the summation of future cash flows. Let us first show how this is done in a spreadsheet program.
You will want to start by creating a spreadsheet such as the above. nclude the parameters we have in the calculator on this page - Face Value, Coupon Rate, Market Interest Rate (or Discount Rate), Years to Maturity and Payments per Year. Then you should use the 'PV' formula (use ';' to separate inputs in OpenOffice, use ',' in Excel). The PV formula works like this:
... as you can see in the above screenshot.
'PV' is, of course, the present value formula. Present value is the concept we hinted to above - the value of a stream of future payments discounted by the conditions in the market today.
Present value, then, is a summation. You can write out each cash flow by hand and calculate it, but this is where computers thrive - feel free to work through some examples with this formula, but know that spreadsheet programs and the JavaScript calculator above are much faster at this sort of work! Here's the formula courtesy Wikipedia:
Where:
Luckily, dirty price is very simple to calculate - you merely calculate the value of the clean price and add the accumulated interest. (And yes, that's as easy as it gets in finance. )
Either way, now you know a lot more about what drives bond pricing in the market - and you have a little more clarity about the theory behind the numbers. Hope you enjoyed the bond pricing calculator and the explanations for how we are calculating the clean and dirty price!
Try our other financial basics and valuation calculators:
On this page is a bond yield to maturity calculator, to automatically calculate the internal rate of return (IRR) earned on a certain bond. This calculator automatically assumes an investor holds to maturity, reinvests coupons, and all payments and coupons will be paid on time.
The page also includes the approximate yield to maturity formula, and includes a discussion on how to find – or approach – the exact yield to maturity.
For this particular problem, interestingly, we start with an estimate before building the actual answer. That's right - the actual formula for internal rate of return requires us to converge onto a solution; it doesn't allow us to isolate a variable and solve.
However, that doesn't mean we can't estimate and come close. The formula for the approximate yield to maturity on a bond is:
( (Annual Interest Payment) + ( (Face Value - Current Price) / (Years to Maturity) ) )
/
( ( Face Value + Current Price ) / 2 )
Let's solve that for the problem we pose by default in the calculator:
100 + ( ( 1000 - 920 ) / 10)
/
( 1000 + 920 ) / 2
=
100 + 8
/
960
=
11.25%
If you've already tested the calculator, you know the actual yield to maturity on our bond is 11.359%.
How did we find that answer?
We calculated the rate an investor would earn reinvesting every coupon payment at the current rate, then determining the present value of those cash flows. The summation looks like this:
Price =
Coupon Payment / ( 1 + rate) ^ 1
+
Coupon Payment / ( 1 + rate) ^ 2
...
+
Final Coupon Payment + Face Value / ( 1 + rate) ^ n
As discussing this geometric series is a little heavy for a quick post here, let us note: for further reading, try Karl Sigman's notes, hosted with Columbia. For most purposes, such as quickly estimating a yield to maturity, the approximation formula should suffice. - any advanced valuation should be done procedurally, on a computer, anyway. The calculator internally uses the secant method to converge upon a solution, and uses an adaptation of a method from Github user ndongo.
A zero coupon bond is a bond which doesn't pay periodic payments, instead having only a face value (value at maturity) and a present value (current value). This makes calculating the yield to maturity of a zero coupon bond straight-forward:
Let's take the following bond as an example:
Price =
(Present Value / Face Value) ^ (1/n) - 1 =
(1000 / 600) ^ (1 / 3) - 1=
1.6666... ^ (1/3) - 1 =
18.563%
Use the Yield to Maturity as you would use other measures of valuation: a factor in your decision whether to buy or avoid a bond.
You can compare YTM between various debt issues to see which ones would perform best. Note the caveat that YTM though – these calculations assume no missed or delayed payments and reinvesting at the same rate upon coupon payments.
For other calculators in our financial basics series, please see:
We got an interesting question about our last piece on high yield corporate bonds, asking whether bond spreads predict stock returns. As the spread between highly rated AAA corporate bonds and below investment grade bonds has recently widened, that sort of information would be worth keeping in your back pocket as you lay out your current investment strategy in the midst of volatile equity markets.
I didn't do a terribly deep dive, and I didn't attempt to eliminate all confounding variables - certainly, if you think this is worth looking into (let me know!), you'd want to at least throw CPI and the Effective Federal Funds rate into the mix. However, as an initial cut, I wanted to come back with a graph showing how the current day yield spread compares to five year subsequent returns on the (price index) S&P 500.
Today we are using two Moody's indices, their AAA and BAA corporate bond yield indices - the Merrill Lynch Bank of America series only go back to the mid 90s (and, again, this is just an initial cut). Although that spread won't be as dramatic as a junk versus highest grade comparison, it will give us an idea of when the spread itself was widening. We mashed it up with Robert Shiller's S&P 500 return data (he extended the series well before the S&P 500 existed). Here's what it looks like:
Can bond spreads predict stock returns?
(5 Year Returns are on the Right Axis, the Baa_Aaa spread is on the left axis.)
For a quick look at total returns, we have a calculator which does dividend reinvestment math on the S&P 500 as well as one for Junk Corporate bonds.
It's tough to say exactly whether the relationship means anything - certainly during the two most notable financial crises in the Great Depression and the Great Recession you would have seen excess returns. The early 1980s also would have seen some nice returns after the widening spread.
However, just eyeballing the chart shows excess returns after WW2 without any sort of a large risk spread, as well as in the 1990s.
My conclusion? Shake your Magic Eight ball (or do the math with different timeframes).
Reply Hazy Try Again
The following is a speculative grade corporate bond return calculator which computes total return of corporate bonds rated CCC or lower. Optionally, it can factor in inflation measured by the Consumer Price Index.
Data is from the Bank of America Merrill Lynch US Corporate Master Index.
To see other corporate bond ratings and returns:
(Note the calculator may load slowly due to the data download the first time you open it each day.)
Data comes from the Bank of America Merrill Lynch Indexes. We pull CCC and lower rated corporate debt every day from St. Louis Federal Reserve’s FRED.
The inflation (CPI) methodology in available on our original any day inflation calculator. It's updated once a month.
Note: data for research purposes only. Please verify any returns with external sources of data. Make allowances for taxes, transaction fees, management fees and other costs which may go along with investing when constructing any models on corporate bonds.
If you enjoyed this, try the Dow Jones Industrial Average, 10 Year Treasury, and S&P 500 calculators.
The following is a medium grade corporate bond return calculator which computes total return of corporate bonds rated BBB, BB, or B. Optionally, it includes estimates for inflation measured by the Consumer Price Index.
It's based on the Bank of America Merrill Lynch US Corporate Master Index.
To see other levels of corporate bond ratings:
(Note the calculator may load slowly due to the data download the first time you open it daily.)
Data is from the Bank of America Merrill Lynch Indexes. We pull B, BB, and BBB rated corporate debt daily from St. Louis Federal Reserve’s FRED.
CPI methodology, including interpolation and extrapolation, is available on our original any day inflation calculator. Interpolations & extrapolations are updated once a month.
Note: this data is for research purposes only - please verify any return numbers with external sources. You should make allowances for taxes, transaction fees, management fees and other costs which may go along with investing.
If you enjoy this type of calculator, try our Dow Jones Industrial Average, 10 Year Treasury, and S&P 500 calculators.
On this page is an investment grade corporate bond return calculator which allows you to compute the total return of investment grade corporate bonds.
It's based on the Bank of America Merrill Lynch US Corporate Master Index for corporate debt in the A to AAA range. It estimates daily returns from 1996 until today, and can adjust for inflation on the CPI index.
For other levels of corporate bond ratings:
(Note the calculator may load slowly due to the data download the first time you open it daily.)
Data is from the Bank of America Merrill Lynch Indexes. We grab AAA, AA, and A rated corporate debt from the St. Louis Federal Reserve's FRED .
The CPI inflation adjustment methodology, including interpolation and extrapolation, is available on our original any day inflation calculator.
Note: results are for educational and research purposes only. Like any index data, individual bond results will vary from aggregate returns. Returns quoted, even if accurate, don't include transactional costs, taxes, and other sources of error like slippage and buy/sell timing.
Caveats aside, we wanted to make it easy to compare the returns on corporate debt versus other asset classes. If you enjoyed this tool, see our total calculators for the Dow Jones, 10 Year Treasuries, and S&P 500. Or, check out other risks linked in the introduction.
A recent comment on one of our CAPE articles recently sent us digging for data on the long term perception of risk in the market. For our purposes, we're interested in risk tolerance and, specifically, the difference in yields between various forms of debt. Why is that important? Well - we could argue all day about valuations in the stock market and whether they matter in the short term to a stock investor.
On the flip side, bonds make a lot more information available to investors - and armed with historical yields we have a lot of data to look at. Let's dive in!
These numbers aren't directly comparable - I'm using 10 year Treasury yields and S&P Index results from Robert Shiller and 30 year AAA and BAA Corporate Bond Yields from Moody's (here are their credit ratings), which target approximately 30 years of maturity. Comparing 10 year yields to ~30 year yields isn't the biggest hack in the world, but please keep it in mind while you review the results. Let's kick it off with the full chart, which is probably more useful to see gyrations than to make any conclusions:
100 Year Risk Premiums
Let me explain the 3 spreads: Baa-Aaa would be the premium demanded for buying Baa rated bonds over Aaa rated ones, and Baa/Aaa - 10Y spreads would be the premium demanded for the respective bond over the 10 Year. And, since you asked, here is the chart for just the last 20 years... so you can actually see the data (what a concept):
20 Year Risk Premiums
Well, the first thing you'll notice is that you'll get the most yield for your money in the scariest times - look, for example, at that spike to a 6+% risk premium for BAA corporate debt during the Great Recession. Also of note is the separation of BAA and AAA corporate debt, which also spiked over 3%. Makes sense, since the most companies will fail under stress during those times.
What else can we say about this sort of behavior? Well, other than that we haven't seen 2008 levels of fear since the Great Depression (note the 'D'), we did have some other 'rising fear' scenarios under Carter and Reagan. Of course, it's also important to call this indicator what it is - a lagging one.
Of course, we recently wrote an article about investor sentiment as measured by the AAII investor survey. In my opinion, that's what we're looking at with this particular risk spread premium - when investors are greedy, the spreads will decrease as people reach for the yield afforded by investments that are seen as too risky during the down times. Viewed from that point of view, our November data shows that investors have been increasingly reaching for yield... but not to the levels seen before the recent financial crisis.
A "fear vs. greed" indicator? Looks like it - but it's also saying that if you're somehow choosing between AAA and BAA corporate debt versus 10 Year Treasuries, your best bet historically is the AAA in this environment - yields compared to the 10 Year are high, and the spread between BAA and AAA isn't enticing. This is, of course, to say nothing about absolute yields (which is low - but inflation expectations are low too, remember). Anyway, that's why we do these think pieces - to find the story behind the story. And in this era of low absolute yields, relative yields are... well, acting somewhat normally.
If you want to use this information to shape your upcoming decisions, here's the statistics on this data:
| Baa-Aaa Spread | Baa-10Y Spread | Aaa-10Y Spread | |
| Average | 1.20% | 2.03% | 0.83% |
| Standard Deviation | 0.71% | 1.01% | 0.53% |
| Maximum | 5.64% | 7.47% | 2.68% |
| Minimum | 0.32% | 0.29% | -0.17% |
| November 2013 | 0.75% | 2.58% | 1.83% |
And the November 2013 readings? AAA - 4.63%, BAA - 5.38%, 10Y - 2.8% (it was 2.88% as of Friday, 12/13).
Here's our related calculator on reinvested 10 Year Treasury returns - we don't yet have one for reinvested corporate debt, but if you ask nicely... 'tis the season!