# 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.

## Answer to relevant Questions

You are involved in a risky business venture where three outcomes are possible: (1) You will lose not only your initial investment ($5000) but an additional $3000; (2) You will just make back your initial investment (for a ...Imagine that you are trying to predict the price of gasoline (regular unleaded) and the price of natural gas for home heating during the next month. Assume you believe that the price of either will stay the same, go up by ...Two gamblers play a version of roulette with a wheel as shown in the file S04_81.xlsx. Each gambler places four bets, but their strategies are different, as explained below. For each gambler, use the rules of probability to ...A machine used to regulate the amount of a certain chemical dispensed in the production of a particular type of cough syrup can be set so that it discharges an average of µ milliliters (ml) of the chemical in each bottle of ...The manufacturer of a particular bicycle model has the following costs associated with the management of this product’s inventory. In particular, the company currently maintains an inventory of 1000 units of this bicycle ...Post your question