FIN 6406-Corporate Finance

Len Lin

Professor’s name:

FIN 6406-Corporate Finance

17/10/2018

Final Exam

Problem 1 [10 points]1.0

1-year call option, S=100, E=87, rf= 3%(annual)I step per year

How much should the call option worth?

The initial and time-t values of the hedge portfolio are given by

HS0-C0= 103H- 50

103H-0

103H-0=103H-50

H=C+- C-/S+-S+ =0/50 = 0.5 shares

Therefore, a portfolio that is long 0.5 shares of stock and short one call is risk-free

0.5So-Co= 0.5*103-50= 26.5

It pays $ 26.5 in all cases

Since S=100, E=87, rf= 3%(annual) a bond that pays 26.5 will be worth today Bo=26.5/1.03= 25.73

This bond is equivalent to the portfolio 0.5So-Co

Therefore, the bond and hedge portfolio must have the same market value;

0.5So-Co=0.5*100-Co=25.73

50-25.73= 24.27

The call price will be $24.27

Problem 7 [10 points]

Consider the following average annual returns for Stocks A and B and the Market. Which of the possible answers best describes the historical betas for A and B

Answer: bA < 0; bB = 0.

Problem 6 [10 points]

We currently have the once-in-a-generation low interest rate environment, and the rates are likely to increase in the next decade. If you recently graduated from college and have a decent job, you have decided to purchase a relative expansive house to your income. Suppose that a bank offers you have three types of mortgages: adjusted rate mortgage (ARM), fixed-rate mortgage with constant payments (FRM) and graduated payment mortgage (GPM). Which type of mortgage should you choose and why?

Answer: One should choose the Fixed-rate mortgage since the interest rates remain the same throughout the term of the loan and since, the rates are likely to increase in the next decade, this choice would be the safest since the current rates are based on the low interest rate environment, while compared to GPM where, payment would start low and increase over time, meaning one will pay more in the next decade. Conversely, the ARM would also not be safe as the initial rate would be fixed for a certain period of time, after which it would adjust itself periodically either monthly or annually and with the anticipated increase in the mortgage rates one would pay more, thus the fixed-rate mortgage is the safest choice.

Problem 8 [10 points]

Suppose that Federal Reserve actions have caused an increase in the risk-free rate, rRF. Meanwhile, investors are afraid of a recession, so the market risk premium-rM-RrF, has increased. Under these conditions, with other things held constant, which of the following statements is most correct and why?

Answer: The prices of all stocks would decline, but the decline would be greatest for high-beta stocks.

Beta in stock tells us about the sensitivity of a stock or underlying with respect to the changes in the stock market. High-beta stocks exhibit greater volatility than broad market index. An increase in the risk-free rate will decrease in the prices of stocks but the decline would be greatest in high-beta stocks since they are very volatile and their prices go up and down very sharply.