4: Valuing BondsexampleSuppose it is late 2015, and with the economy still in
the doldrums from the last recession, most investors
expect very low inflation, perhaps 1% per year. Still-
cautious investors are willing to buy government
bonds as long as they offer a real return of 2%,
so using Equation 4.4a, we would expect nominal
government bond yields to be approximately 3% (1%
inflation + 2% real return).
Imagine that by 2016 the economy is growing
rapidly again. Investors still expect just 1% inflation,
but now their investment alternatives are much
more attractive, and they will only hold government
bonds if they offer a real return of 4%. Under these
conditions, the nominal yield on government bonds
must rise to approximately 5% (1% inflation + 4% real
return).Changes In Issuer risk
When macroeconomic factors change, yields may change simultaneously on a wide range of bonds.
But the market’s required return on a particular bond can also change because the market reassesses
the borrower’s default risk, the risk that the issuer may not make all scheduled payments. For example,
if investors perceive that a certain bond issuer is experiencing financial problems that could make it
difficult for it to repay its debts, the required return will increase and the price of the issuer’s bonds will
fall. Conversely, when the market is more optimistic about a bond issuer’s financial health, the required
return will fall and the issuer’s outstanding bonds will increase in value.
exampleIn the spring and summer of 2010, investors around the world became increasingly concerned about the
financial condition of Greece. Large, sustained budget deficits produced an accumulated debt that was greater
than the nation’s gross domestic product (GDP). From December 2009 to April 2010, yields on 10-year Greek
government bonds rose from 4% to 7% as fears mounted that Greece would not be able to fully repay its debt.
To see the impact that such an increase in yields would have on bond prices, suppose that in November 2009
Greece issued a 10-year bond paying a 4% coupon (two semiannual payments of €20). Because the coupon
rate and the market’s required return were both 4% in November, the bonds sold at a face value of €1,000. Six
months later, just after the first coupon payment, investors required a 7% return on Greek bonds, so the price
of the bonds issued the prior November would be (using Equation 4.3a):
P20
0.035
1
1
(1 0.035)
1, 000
(1 0.035)
0 19 19 794.35
€€
=×− €
+
+
+
=
In just six months, the market price of these bonds dropped €205.65, or more than 20%.
Fortunately, the same effect can work in reverse. In May 2010, the European Union announced a € 100
billion rescue package for Greece. Combined with austerity measures put into place by the Greek government,
the bailout plan seemed to calm the markets, at least to some extent, and Greek bond yields returned to the
4% range. That meant the price of the 10-year Greek bonds sold the prior November would once again return
to their face value.
You might argue that this entire discussion is irrelevant if an investor holds a bond to maturity. If a
bond is held to maturity, there is a good chance that the investor will receive all interest and principal
payments as promised, so any price decrease (or increase) that occurs between the purchase date
and the maturity date is just a ‘paper loss’. Though the tax code may ignore investment gains and
losses until investors realise them, financial economists argue that losses matter, whether investors
realise them by selling assets or whether the losses exist only on paper. For example, when the Greek
default risk
The risk that the bond issuer
may not make all scheduled
payments