8. The Bank of Tinytown has two $20,000 loans that have the following characteristics: Loan A has an expected return of 10 percent and a standard deviation of returns of 10 percent. The expected return and standard deviation of returns for loan B are 12 percent and 20 percent, respectively. Please give me S.D formula and calculate part a) If the correlation coefficient between loans A and B is 0.15, what are the expected return and standard deviation of this portfolio? because model ans have some problem a. 2 31. Calculate the term structure of default probabilities over three years using the following spot rates from the Treasury and corporate bond (pure discount) yield curves. Be sure to calculate both the annual marginal and the cumulative default probabilities. Spot 1 Year 2.0% Treasury bonds BBB-rated bonds Spot 2 Year 3% 5 Spot 3 Year 4.0% 6 4.0 The notation used for implied forward rates is f = forward rate from period 1 to period 2. What formula is used? Treasury bonds (1.03)2 = (1.02)(1 + f2) BBB-rated debt (1.05)2 = (1.04)(1+f:) f = 4.01% = 6.01% (1.04)3 = (1.03)2(1 +12 (1.06)3 = (1.05)-(1 +f) f. = 6.03% = 8.03% Using the implied forward rates, estimate the annual marginal probability of repayment: why p(1.04)=1.02=98.08%? P (1.04) = 1.02 => p. = 98.08 percent P, (1.0601)= 1.0401 => P, = 98.11 percent P, (1.0803) = 1.0603 => P, = 98.15 percent Using marginal probabilities, estimate the cumulative probability of default: , = 1 - (P(P2) = 1 - (.9808)(.9811) = 3.77 percent = 1 - (P, XP, (p) = 1 - (.9808)(.9811).9815) = 5.56 percent