What is the relationship between the expected rate of return for individual investment and the expected rate of return for a portfolio of several investments?

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Reid WolffLv2

26 Feb 2020

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2. The following schedule has eight different expected rates of return and the dollar amounts of the investment projects expected to have each of these return rates.

Expected rate of return	Investment projects (billions)
18%	$ 0
16	10
14	20
12	30
10	40
8	50
6	60
4	70

If the real rate of interest in the economy were 18%, business firms would plan to spend $________ billion for investment, but if the real interest rate were 16%, they would plan to spend $________ for investment.

Should the real interest rate be 14%, and they would still wish to make the investments they were willing to make at real interest rates of 18% and 16%, they would plan to spend an additional $_______ billion for investment, and their total investment would be $________ billion.

If the real rate of interest were 12%, they would make all the investments they had planned to make at higher real interest rates plus an additional $________ billion, and their total investment spending would be $_______ billion.

Suppose you are an investor with a choice between three securities that are identical in every way except in terms of their rates of return and risk, show your work.

Investment A: total return = 15 percent with probability 40percent

total return = 25 percent with probability 60 percent

Investment B: total return = 15 percent with probability 50 percent

total return = 25 percent with probability 50 percent

Investment C: total return = 15 percent with probability 60 percent

total return = 25 percent with probability 40 percent

a- Which investment provides highest expected return? Calculate the expected return of all three investments.

b- Calculate the standard deviation of all three investments.

c- Which of the three investment would you buy? Why? Explain