PLEASE SHOW ALL WORK FOR QUESTIONS I AND QUESTION II

I. Firm A wants to borrow $5,000,000 floating for 3 years; Firm B wants to borrow $5,000,000 fixed for 3 years. Their external borrowing opportunities are shown below: Swap Bank proposes the following interest only swap: Firm A will pay the swap bank annual payments on $5,000,000 with the coupon rate of LIBOR; in exchange, Swap Bank will pay to Firm A the interest payments on $5,000,000 at a fixed rate of 6.30%. Firm B will pay the swap bank interest payments on $5,000,000 at a fixed rate of 6.50% and the swap bank will pay Firm B annual payments on $5,000,000 with the coupon rate of LIBOR+0.14\%. 1. Compute the value of this swap to Swap Bank? (20 points) 2. Compute the value of this swap to Firm A? (20 points) 3. Compute the value of this swap to Firm B? (20 points) II. Based on the article provided to you in class, compute the optimal portfolio weights of two national security markets (2) compute the SHP ratio for each individual national market as well as your optimal international portfolio. Your international portfolio includes two national security markets: U.S. Money Market and Pacific Stock Market. (1) Compute optimal portfolio weights for each national market ( 20 points). (2) Compute SHP ratio for each national market (10 points). (3) Compute SHP ratio for the optimal international portfolio ( 10 points). mean return on the portfolio is the weighted average of the mean asset retums on its assets, as can be seen Table 1 in Equation 2: Average Annual Returns and Risks of Five Funds Monthlv Returns. 1980 to 1998 r=wii where 2 is the mean return on the portfolio and i is the mean return on asset i. Equation 3 shows the variance of the portfolio's return as a weighted average of the standard deviations and correlations of the rehums for its assets: p2=iiwiwf(i rates generally corresponded to periods of low stock prices. On the other hand, the stock markets exhibited respective weights in the portfolio, and if is the similar movements during this period, as reflected in correlation coefficient between the two assets. their positive correlations. Figure 2 plots monthly The standard deviation of the portfolio's return, returns of the three stock indexes from 1980 to 1998 . Which is the square root of variance, is the measure of The positive correlation among their returns is easily risk that is used in all subsequent statistical analysis. seen in the plots. One can also see that the Pacific. Note that the risk of the portfolio depends not just on index has been considerably more volatile than the the standard deviations of the retums on assets that U.S. and European indexes. Given this information on returns, risks, and the correlation coefficient among the assets, the lower correlations of individual assets, we can calculate both the risk of the overall portfolio. This is the reason why the risk and the return on any portfolio consisting of diversification reduces risk. these assets. The return on the portfolio is a weighted The goal of optimization is to find the blend of average of the returns on the assets in it, with the assets that would minimize the standard deviation of weight given to each asset equal to its share in the the portfolio's return for any given level of expected portfolio, as can be seen in Equation 1: return. The optimization problem is usually subject to rp=wri (1) constraints. In particular, the weights must sum to one where rp is the return on the portfolio, ri is the return short-selling). Some institutional investors can, in fact, on asset i, and wi is the proportion of asset i in the sell assets short. However, to keep this example realportfolio (its portfolio weight). Consequently, the allocating the portfolio among easily available mutual PA.B=OAOBCov(A,B) Table 2 Correlations Among the Five Funds' Returns Mrnthil Ratums iafon th togh