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Unformatted text preview: Session 4: Term Structure of Interest Rates A. Both rates (i) are annualised returns (not effective rates), (ii) use the settlement
price as the cost base, and (iii) are total returns accounting for both the coupon
interest component and the capital gain/loss component.
While YTM can be observed in the market and is set by the market, HPR is not
reported to the market and is not set by the market.
While YTM is quoted on the assumption that the coupon interests are all
reinvested at the same rate as the quoted YTM and the bond is held to maturity,
HPR allows for different reinvestment rates for coupon interests received at
different times and the bond to be sold before maturity.
Coupon rate (% pa)
6.0 Time to Maturity (year)
5 YTM (% pa)
6.85 i) The same holding period return of 8.20% is expected.
To compute f(1), the price of the 2-year bond is first computed:
10.5/1.077 + 110.5/1.0772 = $105.014
before applying the present value concept to suggests that
105.014 = 10.5/1.082 + 110.5/[(1+8.20%)(1+f(1))], hence f(1) = 7.15%.
Case 1: Investing in the 2-year bond for 1 year:
Cost (computed earlier)
Under ET, E[r(1)] = f(1) = 7.15%, ∴
Expected selling price = 110.5/(1+ E[r(1)]) = 110.5/1.0715
Expected holding period return = (103.125+10.5)/105.014 -1 = 8.20%
Case 2: Investing in the 1-year bond for 1 year:
Cost = $107.5/1.082
Value of investment after one year = $100 + 7.5
Thus, certain to earn
= 107.5/99.353 – 1 = $99.353
= 8.20% ii) Investing in the 2-year bond for 1 year:
Cost (computed earlier)
Since the expected interest rate on a one year bond in one year’s time = f(1)-LP
Expected selling price = 110.5/1.0665
Expected holding period return = (103.608+10.5)/105.014 -1 = 8.66%
Not certain. We need to wait for one year before we can observe the actual
interest rate on the one-year bond and know the actual selling price. As long
as the actual rate is different from that expected, the actual selling price and
hence the HRP will be different. 1 iii) Investors holding bonds for a period shorter than the maturity will face price
risk. Under the liquidity premium theory, investors are assumed to be risk
averse. Hence they demand a liquidity premium (or additional return) to
offset the risk exposure to uncertain selling price.
iv) 10.5/1.077+110.5/1.0772 = $105.014 = 10.5/1.082 +110.5/(1+y2)2, y2 = 7.675%.
v) 8/1.074+8/1.0742+108/1.0743 = 101.563= 8/1.082+8/(1.07675)2+108/(1+y3)3,
y3 = 7.363%.
C. Coupon stripping means splitting the coupon payments and face value of a bond
into individual cash flows. These cash flows are then repackaged and sold
separately as individual zero coupon bonds.
Merchant bankers and financial institutions owning an inventory of bonds could
perform this activity to earn a profit margin. Despite the demand for zero coupon
bonds due to its risk free attribute if held to maturity and tax-deferral advantage,
the Commonwealth government does not issue zero coupon bonds. Hence there
is niche market to support the coupon stripping activity.
D. According to the expectations theory, investors are risk neutral. Hence they rank
investments on the basis of expected return. For a given holding period, since
bonds with different times to maturity are expected to provide the same return,
investors are indifferent between bonds with different times to maturity.
According to the liquidity premium theory, investors are risk averse. Hence they
rank investments on the basis of expected return and risk. For a given holding
period, although the long term bonds are expected to provide more return than
the short term bond, the long term bonds also expose investors to more price risk
as interest rates are less predictable. Thus long term bonds are preferred if and
only if the investor perceives that the additional return expected from the long
term bond more than offsets the exposure to price risk.
E. According to the liquidity premium theory:
f(n,t) = E[r(n,t)] + E[LP(n,t)]
where f(n,t) is the future interest rate of an n-year bond in t years’ time as implied
by the term structure, E[r(n,t)] is the future interest rate of an n-year bond in t
years’ time as expected by the market, and E[LP(n,t)] is the liquidity premium
associated with the forecast.
As it is harder to predict further into the future, the amount of price risk due to
inaccurate forecasts increases with t and a larger liquidity premium is expected.
It is also harder to predict the rate for long term bonds than the rate for short term
bonds. Hence, the amount of price risk due to inaccurate forecasts increases with
n and a larger liquidity premium is expected. 2 ...
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