term%20structure - Session 4: Term Structure of Interest...

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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. B. Coupon rate (% pa) 7.5 10.5 8.0 6.0 6.0 Time to Maturity (year) 1 2 3 4 5 YTM (% pa) 8.20 7.70 7.40 7.00 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) = $105.014 Under ET, E[r(1)] = f(1) = 7.15%, ∴ Expected selling price = 110.5/(1+ E[r(1)]) = 110.5/1.0715 = $103.125 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 = $107.50 = 8.20% ii) Investing in the 2-year bond for 1 year: Cost (computed earlier) = $105.014 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 = $103.608 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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This note was uploaded on 10/29/2010 for the course FINS 2624 taught by Professor Hneryyip during the Three '10 term at University of New South Wales.

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