E. Yield
Yield is the percentages return your bond investment promises at any given price. In its most simple form - known as ‘current yield’ or ‘coupon yield’ - it can be expressed with this formula:
Current Yield = Coupon/ Price |
Take a ‘straight bond’ with a face value of $1000 paying a 5% coupon. If you were to buy it for $1,000, the current yield would simply be 5% ($50 / $1,000). So, when you buy a bond for face value, the yield is simply the coupon, or interest rate.
However current yield is the most simplistic approach to yield and does not take into your coupon gains on the bond. Hence “yield to maturity" is the conventional yield calculation. This represents the total return you can expect if you buy a bond at a given price and hold it until it matures.
The YTM is:
• The uniform discount rate which makes the present value of a bond’s future cash flows equal to its quoted dirty price
• The return that would be achieved on the bond if:
-it is bought at the quoted price
-and it is held until maturity
-and any coupons received are reinvested at the same rate
• The internal rate of return (IRR) on all of the bond's cash flows, including the initial outlay
However current yield is the most simplistic approach to yield and does not take into your coupon gains on the bond. Hence “yield to maturity" is the conventional yield calculation. This represents the total return you can expect if you buy a bond at a given price and hold it until it matures.
The YTM is:
• The uniform discount rate which makes the present value of a bond’s future cash flows equal to its quoted dirty price
• The return that would be achieved on the bond if:
-it is bought at the quoted price
-and it is held until maturity
-and any coupons received are reinvested at the same rate
• The internal rate of return (IRR) on all of the bond's cash flows, including the initial outlay
Limitations of YTM
YTM takes into account all the three components of return:
• The periodic coupon payments
• Interest earned on the reinvestment of the coupons received
• A capital gain or loss realized when the bond is redeemed
But it makes two fundamental assumptions:
• That the investor actually holds the bond until maturity (there is no guarantee that the bond can be sold at par before maturity)
• That the coupons received will all be reinvested at the bond's YTM.
YTM is therefore a theoretical calculation: it does not compute the actual return that an investor will make on the bond, even if it was held to maturity. The actual return will depend on future reinvestment rates achieved.
Nevertheless, YTM is useful as a means of comparing the return on bonds with similar maturity and credit quality: a bond may be considered cheap if it yields more than a comparable issue. In this context, assumptions about future reinvestment rates may be less critical, since the same reinvestment rates will apply to all the bonds being compared.
Example – Zero Coupon
Security: Zero maturing in exactly 12 years
Compounding: Semi-annual
Coupon
Price: 25.00
What is the yield to maturity on this zero coupon bond?
100/25=4
{(4)^(1/24)} -1= Semiannual return= 0.5946
Annual return= 11.89%
This is also referred to as “compound yield” as it takes into account the “compounding effect”
• The periodic coupon payments
• Interest earned on the reinvestment of the coupons received
• A capital gain or loss realized when the bond is redeemed
But it makes two fundamental assumptions:
• That the investor actually holds the bond until maturity (there is no guarantee that the bond can be sold at par before maturity)
• That the coupons received will all be reinvested at the bond's YTM.
YTM is therefore a theoretical calculation: it does not compute the actual return that an investor will make on the bond, even if it was held to maturity. The actual return will depend on future reinvestment rates achieved.
Nevertheless, YTM is useful as a means of comparing the return on bonds with similar maturity and credit quality: a bond may be considered cheap if it yields more than a comparable issue. In this context, assumptions about future reinvestment rates may be less critical, since the same reinvestment rates will apply to all the bonds being compared.
Example – Zero Coupon
Security: Zero maturing in exactly 12 years
Compounding: Semi-annual
Coupon
Price: 25.00
What is the yield to maturity on this zero coupon bond?
100/25=4
{(4)^(1/24)} -1= Semiannual return= 0.5946
Annual return= 11.89%
This is also referred to as “compound yield” as it takes into account the “compounding effect”
Coupon bearing:
Example: Suppose your bond is selling for $950, and has a coupon rate of 7%; it matures in 4 years, and the par value is $1000. What is the YTM?
The coupon payment is $70 (that's 7% of $1000), so the equation to satisfy is
The coupon payment is $70 (that's 7% of $1000), so the equation to satisfy is
R solves for 8.53%
The inverse relationship
A bond’s price and a bond’s yield are inversely related; that is to say, when a bond’s price falls its yield rises and vice-versa. Why?
Assume you were to buy 5% coupon bond for $1000, the current yield would simply be 5% ($50 / $1,000). But if the price drops to $950, the yield - for anyone who bought the bond for $950 - rises to 5.26% ($50 / $950). Intuitively, this is because the guaranteed coupon - $50 - is now a greater percentage of the price of the bond.
Conversely, if you buy the bond for $1000 and its price rises to $1050, the yield - for anyone who buys the bond at $1050 - falls to 4.76% ($50 / $1050). This is because the guaranteed coupon - $50 - is now a smaller percentage of the price of the bond.
This simple relationship raises all sorts of important questions. For now though we will consider just one: If yields and prices move in opposite directions, why are both high yields and high prices considered good things? The answer depends on your perspective.
If you are a bond buyer, high yields are what you want, because you want to pay $950 for that $1,000 bond.
Once you own the bond, however, you want its price to rise. You have already locked in your yield, and if the price rises, it can only be a good thing - especially if you need cash and want to sell the bond to get it.
Assume you were to buy 5% coupon bond for $1000, the current yield would simply be 5% ($50 / $1,000). But if the price drops to $950, the yield - for anyone who bought the bond for $950 - rises to 5.26% ($50 / $950). Intuitively, this is because the guaranteed coupon - $50 - is now a greater percentage of the price of the bond.
Conversely, if you buy the bond for $1000 and its price rises to $1050, the yield - for anyone who buys the bond at $1050 - falls to 4.76% ($50 / $1050). This is because the guaranteed coupon - $50 - is now a smaller percentage of the price of the bond.
This simple relationship raises all sorts of important questions. For now though we will consider just one: If yields and prices move in opposite directions, why are both high yields and high prices considered good things? The answer depends on your perspective.
If you are a bond buyer, high yields are what you want, because you want to pay $950 for that $1,000 bond.
Once you own the bond, however, you want its price to rise. You have already locked in your yield, and if the price rises, it can only be a good thing - especially if you need cash and want to sell the bond to get it.