6 7 question 7 consider two assets a and b asset a is

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Question 7 Consider two assets: A and B. Asset A is a stock. For the stock, there is a probability of 0.7 that next period each shareholder will receive $5 as dividends and that the stock price immediately after the dividend has been paid (the ex-dividend price) is $120. With probability 0.3 next period each shareholder will receive $2 as dividends and the ex-dividend price will be $60. Asset B is a zero coupon bond with no default risk, that will pay its holder a payoff $50 next period (the face value is $50). a. If investors are risk neutral which asset of the two will have a higher price? Which asset will have a higher expected return? Answer: When investors are risk neutral they simply prefer the asset with the higher expected return and do not care about the riskiness of assets. In 8
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this case they also use the risk free rate to discount all future cash flows because they do not demand a compensation for risk. The expected payoff of A is 10 . 106 ) 60 2 ( 3 . 0 ) 120 5 ( 7 . 0 ) ( payoff E Whereas the expected payoff of asset B is 50. So asset A will have a higher price in the market (given that both assets are discounted by the risk free rate). As for expected return: both assets will have the same expected returns . Because investors do not care about risk in this case, they will only demand compensation for the time value of money and not for risk. This again means they will discount future cash flows by the risk free rate. Therefore the expected returns will also be the risk free rate. To illustrate this consider the price of asset A: P A = 106.10 1 + r f = ¿ E ( r A ) = E ( payoff ) Price at t 1 = r f b. If investors are mean-variance investors. That is, the like expected return and dislike standard deviation, can we say which asset will have a higher price? Which will have a higher expected return?
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