Question

(1) One, two, and three year maturity, default free, zero coupon bonds have yields to maturity of 7%, 8%, and 9%, respectively. What is the implied 1-year forward rate 1 year from today?

(2) Consider a two-asset portfolio with $10 invested in each asset. The mean returns of the two assets are 10% and 15%. The correlation of returns is 50%. The standard deviation of returns is 20% and 30%, respectively. What is the 99% VaR of this portfolio?

(3) Assuming annual compounding, the prices of a one-year 4% coupon bond and a two year 5% coupon bond are $101 and $99, respectively. The fair price of a two-year 6% coupon bond would be what?

(4) Assuming annual compounding, the prices of a one-year 4% coupon bond and a two-year 5% coupon bond are $101 and $99 respectively. The forward rate between one and two years is what?

(5) You are given two discount bonds of one-year and two-year maturities, with prices of $95 and $90 respectively. A third bond of three-year maturity and an annual coupon of 8% is trading at par. What is the three-year continuously compounded zero-coupon rate?

(6) True or false: If a firm's credit spread increases, the firm's assets have decreased in value and the risk of its assets have increased.

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Answer 1:
In this case, we have been given the annual rates.
Given that the yield to maturity of zero coupon bond with 1 year to maturity is 7% and that with 2 years to maturity is 8%.
The implied 1 year forward rate 1 year from today is the rate at which the proceeds from the bond that matures in one year would be invested so that the total annual return for 2 years is 8%. This can be...

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