1) The current price of a stock is $32, and the annual risk-free rate is 6%. A c

Question

1) The current price of a stock is $32, and the annual risk-free rate is 6%. A call option with a strike price of $29 and 1 year until expiration has a current value of $5.30. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Round your answer to the nearest cent.

2) You have a $2 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.05. You are considering selling $100,000 worth of one stock with a beta of 1.15 and using the proceeds to purchase another stock with a beta of 1.35. What will the portfolio's new beta be after these transactions? Round your answer to two decimal places.

3) A Treasury bond that matures in 10 years has a yield of 4%. A 10-year corporate bond has a yield of 9%. Assume that the liquidity premium on the corporate bond is 0.7%. What is the default risk premium on the corporate bond? Round your answer to two decimal places.

Explanation / Answer

1. Stock price + put price = call price + strike price*e^(-risk free rate)

i.e. 32 + put price = 5.30 + 29*e^(-6%)

So put price = 5.30 + 29*e^(-6%) - 32 = 0.61

2. New portfolio beta = old portfolio beta + stock value / portfolio value * (new stock beta-old stock beta)

= 1.05 + 100,000/2,000,000*(1.35-1.15) = 1.06

3. (1+treasury bond yield)*(1+liquidity premium)*(1+default risk premium) = (1+corporate bond yield)

Solving, we get (1+4%)*(1+0.7%)*(1+default risk premium) = (1+9%)

So, default risk premium = 4.08%

Hope this helped ! Let me know in case of any queries.

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