Arbitrage Pricing Theory

QUESTION 1

Explain the following terms in the context of portfolio theory and the CAPM (please use diagrams if necessary):

1) Mean Variance Efficient portfolio

2) Market Efficient Frontier

3) Capital Market line

4) Tangent Efficient Portfolio

5) Arbitrage Pricing Theory

QUESTION 2

“The greater number of securities in the portfolio the lower the risk “Is the statement true or false? Using a graph explain why?

QUESTION 3

1. a) I currently have £20,000 but require £35,000 in 5 years’ time.
2. What rate of interest payable annually, must I receive on the £25,000 to make this possible?
3. Discuss the difference between nominal interest rate and effective interest rate.

• What is the equivalent rate payable weekly? Show your workings including the rate timeline with cash flows.

1. b) you wish to have £30,000 in 4 years’ time for the deposit on a property. You can invest at of 8% compounded quarterly. How much should you save each quarter beginning immediately? Show your workings including the timeline with cash flows.

QUESTION 4

1. Explain what is meant by convexity with regard to the price-yield relationship, and how it varies between callable and non-callable bonds. Also, what is meant by the yield to call?
2. A non-callable 5 years UK government bond pays semi-annually coupons. The face value is £10,000, the annual coupon rate is 8% and the yield to maturity is 10% per year.

Calculate the annualised values for both Macaulay’s duration and the modified duration, and show how the latter may be used to estimate the pricing impact of a change in the yield from 8% to 4%.

QUESTION 5

A European put option on a non-dividend paying stock with a strike price of £40 ad an expiration date in six months’ costs £1. The stock price is £37 and the risk-free interest rate is 5% per annual compounded continuously.

1. what is the lower bound for this put option?
2. Identify the arbitrage opportunity open to a trader
3. What is the minimum profit you would realise by arbitraging?