Question

15-4     Suppose you win the Florida lottery and are offered a choice of $500,000 in cash or a       gamble in which you would get $1 million if a head is flipped but zero if a tail comes up.

Suppose you take the sure $500,000. You can invest it in either a U.S. Treasury bond that will return $537,500 at the end of one year or a common stock that has a 50-50 chance of being either worthless or worth $1,150,000 at the end of the year.

1. What is the expected dollar profit on the stock investment? (The expected profit on the T-bond investment is $37,500.)
2. What is the expected rate of return on the stock investment? (The expected rate of return on the T-bond investment is 7.5 percent.)
3. Would you invest in the bond or the stock?
4. Exactly how large would the expected profit (or the expected rate of return) have to be on the stock investment to make you invest in the stock, given the 7.5 percent return on the bond?
5. How might your decision be affected if, rather than buying one stock for $500,000, you could construct a portfolio consisting of 100 stocks with $5,000 invested in each? Each of these stocks has the same return characteristics as the one stock—that is, a 50-50 chance of being worth either zero or $11,500 at year-end. Would the correlation between returns on these stocks matter?

Answer 1

What is the expected dollar profit on the stock investment? (The expected profit on the T-bond investment is $37,500.)

Expected Dollar Profit = Higher Return * Probability + Lower Return * Probability - Investment

Expected Dollar Profit = 1150000 * 50% + 0 * 50% - 500000

Expected Dollar Profit = $75000

What is the expected rate of return on the stock investment? (The expected rate of return on the T-bond investment is 7.5 percent.)

Expected Rate of Return = Dollar return / Investment = 75000 / 500000 = 15%

Would you invest in the bond or the stock?

I would invest in Stock as it give higher return than Treasury Bond

Exactly how large would the expected profit (or the expected rate of return) have to be on the stock investment to make you invest in the stock, given the 7.5 percent return on the bond?

Exactly how large would the expected profit = Investment * Treasury return

Exactly how large would the expected profit = 500000 * 7.50%

the expected profit = $37500

How might your decision be affected if, rather than buying one stock for $500,000, you could construct a portfolio consisting of 100 stocks with $5,000 invested in each? Each of these stocks has the same return characteristics as the one stock—that is, a 50-50 chance of being worth either zero or $11,500 at year-end. Would the correlation between returns on these stocks matter?

Correlation between stocks will matter due to the fact that each stock might go up or down but how much of a stock return goes up when the other stock goes up or down is very much required to make a decision.

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