Price and Yield have an inverse relationship – when one goes up, the other comes down.
In our previous blog, we defined yield and described how and why yields differ with changes in the risk-free rate.
But did you know that there are actually several ways that you can measure yield?
Let’s start with the basics!
A coupon payment tells us how much money we will earn when we acquire a bond at a price of par (100%).
Do you remember the formula to calculate yield?
Coupon / Bond Price = Yield.
For example, what would be the yield of a bond with a 5% coupon trading at 110?
5% (Coupon) / 110 (Bond Price) = 4.55% (Yield).
Remember that price and yield have an inverse relationship, so if a bond has a 5% coupon but it is trading at 90, the current yield would be 5.6%.
This makes sense because a bond is always paid back at par at maturity – unless a company defaults.
In simpler terms, the higher the bond trades, the lower the return.
This is because you are effectively spreading the additional purchase price across the life of the bond.
In contrast, the lower a bond trades, the higher the return.
Low price bonds benefit from “pull to par” – where the gain in price is spread over the remaining life of the bond.
Yield to Maturity (YTM)
This is a more accurate measure of yield and it is essentially an annualised internal rate of return.
YTM is the total return you would receive from a bond if you held it to maturity.
You will often hear of YTM from investors due to it being a comprehensive measure.
It takes into account income generated from coupons until maturity, as well as any capital gain/loss should the bond not have been bought at par (100%).
Buying a bond means undergoing a series of cash flows
The first is negative because you are buying the bond.
All other future cash flows are positive because you would be receiving the periodic coupon and periodic coupon plus par.
Now imagine you placed all those cash flows out in a long straight line stretching into the future to the maturity date.
We can equate them to the current bond price by “discounting” them using a specified rate and adding them up.
This essentially adjusts a cash flow for its riskiness.
Do you remember the reinvestment risk?
As cash flows move further into the future there is more uncertainty around whether we will receive them or not.
Discounting adjusts this by multiplying a cash flow by a “discount factor”.
What’s a discount factor?
1 / (1 + Risky Rate) – where the risky rate is the return demanded by the market.
The risky rate is also compounded in order to take account of time.
For example, at year one the discount factor is (1 + Risky Rate) ^ 1.
At year two the discount factor is (1 + Risky Rate) ^ 2, and so on.
After the sum of cash flows is multiplied by the relevant discount factor, we finally arrive at the bond price or present value.
The risky rate that ensures the discounted future cash flows add up to the bond price is the YTM.
As with the current yield, this is naturally higher than the coupon if the bond is trading below par and vice versa if the bond is trading above par.
Yield to Call (YTC)
This is the yield that an investor will receive if the bond is paid back at a given call date.
As you may remember, bonds can be called back before their maturity date.
In the callable bond’s documentation, there is a series of dates that are set out to an investor, giving them the right, but not the obligation, to retire the debt at a specified price.
That price is typically par plus 100% of the coupon on the first call date, par plus 50% of the coupon on the second call date, par plus 25% of the coupon on the third call date, and generally par from every call date onwards.
For the callable bond, for each of the call dates, you can draw a line that captures all the cash flows that one expects to receive, as well as the initial purchase price.
The length and number of cash flows on that line depend on how far away that call date is.
For each line, the redemption value is the respective call price.
The risky rate needed to equate the future cash flows with the current price is therefore different depending on which call date is being considered.
This makes sense given each call scenario has a different set of cash flows.
Yield to Worst (YTW)
This measurement of yield is more relevant than YTC as it is the lowest yield an investor will receive buying a callable bond.
Let’s take a look at the following example.
Suppose a bond is callable at 103, 101.5, and 100.
The current price of the bond is 104 – is it trading above the call price.
This indicates that the market thinks that the bond will be called on the first call date.
In this case, the YTW will equal the yield to first call.
If, however, the bond is trading at par, the YTW will equal the YTM and reflect the market’s view that the bond will not be repaid before maturity.
A key point to consider when buying a callable high yield bond is the estimated repayment date of your investment.
When matching your investments to your desired investment time horizon, use YTW.
Our next blog post…
We will have an introduction to fundamental analysis and look at the three main financial statements.
As usual, all of this content can be found on our free Bond Academy, a CPD accredited course that offers 5 hours of CPD activity.
If you have any ideas on topics that you’d like for us to talk about, please email me: email@example.com.