Stan plans to invest $100,000 in either a risk-free bond or a portfolio of 100 stocks. If he buys the bond, it will be worth $107,000 at the end of one year, for a guaranteed return of 7 percent. Alternatively, he could put $1,000 each into 100 different stocks. Each stock has a 50-50 chance of being worth either $2,300 or $0 at the end of the year, so the expected return on each stock (and the whole portfolio) is 15 percent. Which of the following should make Stan more likely to invest in the stock portfolio? The stocks are uncorrelated with each other (r = 0).

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Business

Callie Jensen

15 September, 11:28

Stan plans to invest $100,000 in either a risk-free bond or a portfolio of 100 stocks. If he buys the bond, it will be worth $107,000 at the end of one year, for a guaranteed return of 7 percent. Alternatively, he could put $1,000 each into 100 different stocks. Each stock has a 50-50 chance of being worth either $2,300 or $0 at the end of the year, so the expected return on each stock (and the whole portfolio) is 15 percent. Which of the following should make Stan more likely to invest in the stock portfolio? The stocks are uncorrelated with each other (r = 0).

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Eliezer Bradford · Answer 1

The stock investment is preferred

Explanation:

The bond give a holding period yield of 14% which is calculated thus:

holding period yield = (p1-p0) / p0+return of 7%

= (107,000-100,000) / 100,000+7%

=7%+7%

=14%

The stock investment of 15% is preferred over the bond return of 14%, since the stock portfolio comprises of assets that are not correlated which implies adverse performance in one stock asset does not affect the performance of others, invariably the 15% return is near guarantee.