# Question: The return on a portfolio during a period is defined

The return on a portfolio during a period is defined by

PVend – Pvbeg / PVbeg

Where PVbeg is the portfolio value at the beginning of a period and PVend is the portfolio value at the end of the period. Suppose there are two stocks in which you can invest, stock 1 and stock 2. During each year there is a 50% chance that each dollar invested in stock 1 will turn into $2 and a 50% chance that each dollar invested in stock 1 will turn into $0.50. During each year there is also a 50% chance that each dollar invested in stock 2 will turn into $2 and a 50% chance that each dollar invested in stock 2 will turn into $0.50.

a. If you invest all your money in stock 1, find the expected value and standard deviation of your one year return.

b. Assume the returns on stocks 1 and 2 are independent random variables. If you put half your money into each stock, find the expected value and standard deviation of your one-year return.

c. Can you give an intuitive explanation of why the standard deviation in part b is smaller than the standard deviation in part a?

d. Use simulation to check your answers to part b. Use at least 1000 trials.

PVend – Pvbeg / PVbeg

Where PVbeg is the portfolio value at the beginning of a period and PVend is the portfolio value at the end of the period. Suppose there are two stocks in which you can invest, stock 1 and stock 2. During each year there is a 50% chance that each dollar invested in stock 1 will turn into $2 and a 50% chance that each dollar invested in stock 1 will turn into $0.50. During each year there is also a 50% chance that each dollar invested in stock 2 will turn into $2 and a 50% chance that each dollar invested in stock 2 will turn into $0.50.

a. If you invest all your money in stock 1, find the expected value and standard deviation of your one year return.

b. Assume the returns on stocks 1 and 2 are independent random variables. If you put half your money into each stock, find the expected value and standard deviation of your one-year return.

c. Can you give an intuitive explanation of why the standard deviation in part b is smaller than the standard deviation in part a?

d. Use simulation to check your answers to part b. Use at least 1000 trials.

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