Question

Smart Investor lives in a small country with only one publicly traded company, Supertech. This country had a functioning banking system and Smart Investor can borrow money from a bank, or put money in a savings account. The interest rate is 6%. Smart Investor has $10,000 that he wants to invest for one year. Looking at historical data and studying the current prospects of Supertech, Smart Investor makes the following scenario: the rate of return on Supertech can be 20% with probability 0.3, 10% with probability 0.4, 0% with probability 0.2 and -10% with probability 0.1. i. Compute the mean and standard deviation of rate of return of Smart Investor’s portfolio for the following scenarios: a) He invests his $10,000 in shares of Supertech b) He puts $10,000 in a savings account c) He invests half of his money in shares of Supertech and puts the other half in a savings account d) He borrows $5,000 for a year from a bank and invests $15,000 in shares of Supertech e) He borrows $20,000 dollars and invests $30,000 in shares of Supertech 1 ECON 131 ii. More generally compute the mean and standard deviation of the rate of return of Smart Investor’s portfolio if he invests a proportion ?⁡(? ≥ 0) of his money in shares of Supertech iii. Graph the possible combinations (?, ?) of expected value-standard deviation that Smart Investor can obtain by choosing an appropriate portfolio. Mark points A,B,C,D,E corresponding to the scenarious (a)-(e) from question (i). Explain why this graph illustrated the trade-off risk versus returns which is characteristic of financial markets. iv. Smart Intestor decided that he will not tolerated more that 5% standard deviation on his future rate of return. What is the maximum proportion ?? of stock that he can have in this portfolio? What is the expected rate of return that he can get for this amount of risk? v. Smart Investor wants to be absolutely sure that he will recover at least $10,000 next year in any circumstance. This he makes the precise calculation of what he will get next year in every possible circumstance if he invests a proportion ?? in Supertech. What does he find? Will he decide after all to follow the strategy ???

Answer 1

Given the interest rate of the savings account is 6%. Smart Investor has $10,000 that he wants to invest for one year. It is known that the rate of return on Supertech can be 20% with probability 0.3, 10% with probability 0.4, 0% with probability 0.2 and -10% with probability 0.1

a) The expected return of Smart Investor’s portfolio

The standard deviation of rate of return of Smart Investor’s portfolio

The standard deviation is .

b) Expected return of Smart Investor’s portfolio when he invests the whole amount in bank is

The standard deviation is . Since the savings bank interest rate is constant.

c) When he invests half of his money in shares of Supertech and puts the other half in a savings account,

The standard deviation is .

d) He borrows $5,000 for a year from a bank and invests $15,000 in shares of Supertech

The standard deviation is .

We are required to solve only 4 parts. Please post the remaining questions as another post.