Reference no: EM131003284

1) Compare the interest rate risk of a noncallable 10-year Treasury coupon bearing bond with a mortgage-backed pass-through security with prepayments related to the level of interest rates - lower market interest rates raise the rate of prepayments.

Discuss how the changes in cash flows, arising from prepayments, on a mortgage-backed security affect the duration of such securities. HINT: consider the coupon effect on duration.

Macaulay Duration Measure:

DM = ∂P/∂y (1 + y)/P, For a coupon - bearing bond: Dm = (_t=1Σ^MtC/(1 + y)^t + MF/(1 + y)^M) / ( _t=1Σ^MC/(1 + y)^t + F/(1 + y)^M)

A more complete approximation to the proportional change in price of a bond with respect to a change in yield to maturity takes into account the convexity of the price-yield relationship for the bond:

dP/P = ∂P/∂y. 1/Pdy + 1/2 ∂²P/∂²y 1/P dy²

where P = Price, C = coupon, F = Face value, y = Yield to maturity, M = maturity (years), t = time (year), dP is the total change in price, and is the partial change in price with respect to a change in yield to maturity. The second term, excluding the dy², is the convexity effect.

2) Data on weekly stock prices for Microsoft Corporation, Exxon Mobil Corporation and the S&P 500 Index were used to compute the following historical volatility and expected return. Using these results, answer the following questions:

The historical returns volatility (standard deviation of returns) at an annualized rate for each stock are: MSFT= 0.182, XOM= 0.120 and S&P500 = 0.108. The expected return for each stock and the index at an annual rate for MSFT, XOM and S&P500 is respectively:

                                                                                                                        0.136    0.308    0.105

a. Using the computed β (beta) of 0.997 for MSFT and 0.508 for XOMand expected return for each stock and the S&P 500 index over the past year, draw the Securities Market Line (SML) using a risk-free rate of 5.37 percent based on the 3-month Libor rate at the time. Do each of the stocks fall on the SML? Analyze their relative position and which stock is the best buy and why.

HINT: Use the average return of the S&P 500 stock index provided above as the expected return for the market.

b. Using the data in above and in a. and assuming the average return on the S&P 500 index is a representation of market expected return and risk, compute the slope of the Capital Market Line (CML) when the risk-free rate is approximated by the Libor rate given in a. From your results, what is the market price of risk?