Reference no: EM132535263
Suppose that we have a new security available for us to invest in, with a 1-year term to maturity. Let D be the random cash flow (assumed to be non negative) produced by this new security at the end of 1 year. Let Rf be the risk free interest rate and let E(Rm) be the expected return on the market portfolio.
Consider the following formulae for valuing the new security's cashflow (EQ means compute expectation using the "risk neutral distribution", while E means the "real world" expectation).
(1) Discounted Expected Value Using the risk free rate P = E(D) 1+ Rf
(2) Discounted Expected Value Using a risk adjusted rate (CAPM pricing ) P = E(D)
1+Rf +β(E(Rm)-Rf )
(3) Risk Neutral Pricing: P = EQ (D) 1+ Rf
Assuming that the new security has returns which are positively correlated with the market portfolio's returns,
(i) Explain why formula 1 will usually overprice the new security. In what circumstances would it give the correct valuation?
(ii) Discuss the nature of the adjustments to either the discount rate or the payment being discounted in formulae 2 and 3 compared to formula
1. What is being adjusted? Is it an upwards or a downwards adjustment?
(iii) Under what circumstances is it appropriate to use each of these formulae to value a security / cash flow?
(iv) Your neighbour bought a ticket in a lottery and is now desperate to sell it due to a personal crisis and is desperate to sell it to you. If the ticket is the winning ticket then the payoff will be $20.6m. The probability of winning is quite low, at 0.01%. Assume a risk free rate of 12% p.a. convertible quarterly, and a term of 3 months until the lottery result is known and the payoff is made, use the capm formula to price the ticket. Explain why the beta of the ticket should be zero.
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