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# Single stock portfolio / 100 stock portfolio

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Your eccentric uncle died and left you \$100,000. However, the will stipulated that the entire amount must be invested in common stocks. Specifically, \$50,000 must be invested in a single stock (a one-stock portfolio) and the other \$50,000 must be invested in a 100-stock portfolio. You are very risk averse, so you want to minimize the riskiness of each \$50,000 investment.

a. Describe the kind of stock you would choose for your single-stock portfolio.
b. What types of stock would you choose the stocks for your 100-stock portfolio?

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#### Solution Preview

a. Describe the kind of stock you would choose for your single-stock portfolio?

If a stock is held alone, then the measure of risk is the standard deviation of returns. Higher the standard deviation, more is the risk. ...

#### Solution Summary

The solution explains which kind of stock to be added in a single stock portfolio and in a 100 stock portfolio.

\$2.19
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## Finance Practice Solution

You have won a lottery have been offered (1) \$0.5 million, or (2) a
gamble in which you would receive a \$1 million if a head were flipped and \$ 0 if a tail came
up.

a. What is the expected value of the gamble?
b. Would you take the sure \$0.5 million or take the gamble? Why?
c. If you choose the sure \$0.5 million are you a risk taker or risk averter?
d. Assume that you actually take the sure \$0.5 million; you can invest it in either a US Treasury
bond that will return \$537,500 at the end of a year or a common stock that has a 50&#8725;50 chance of being either worthless or worth \$1,150,000 at the end of the year.

(1) Calculate the expected dollar profit on the stock investment. (The expected profit on
the US Treasury bond is \$37,500.)
(2) Calculate the expected rate of return on the stock investment. (The expected rate of
return on the US Treasury bond is 7.5%.)
(3) Would you invest in the bond or the stock? Why?
(4) Exactly how large would the expected profit (or expected rate of return) have to be on
the stock investment to make you invest in the stock, given the 7.5% return on the
bond?
(5) How might your decision be affected if, rather than buying one stock for \$0.5 million,
you could construct a portfolio of 100 stocks with \$5,000 invested in each stock? Each
of these 100 stocks has the characteristics as the one stock - that is, a 50&#8725;50 chance of being
worth either \$ 0 or \$11,500 at year end. Would the correlation between these stocks
matter? Explain.

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