Question

An investor buys 1 share of ABC Ltd at the price of $32 on December 1, 2019. The firm is not expected to pay any dividends. Consider the following three possible scenarios for the share price on December 1, 2020: $50 with a probability of 20% $34 with a probability of 50% $27 with a probability of 15% $20 with a probability of 15% a) Calculate the expected return for holding the share for a year. b) Calculate the variance of return and standard deviation of return. c) Explain the concept of diversification. Explain the benefit of diversification and how it works. d) “The standard deviation of a portfolio's return can be reduced to zero by holding all the securities in the market.” True or false? Explain.

Answer 1

a. The expected return can be calculated by calculating the expected price. Expected price will be = 0.2 x 50 + 0.5 x 34 + 0.15 x 27 + 0.15 x 20 = $34.05. Hence, the expected return is = (34.05 - 32)/32 = 6.406%

b. The variance of return will be calculated by finding the deviation of each return from the mean. We first find all the returns. (50-32)/32 = 56.25%, (34-32)/32 = 6.25%, (27-32)/32 = -15.625%, (20-32)/32 = -37.5%. Now, we use the variance formula: Variance = summation(pi x (xi-xmean)2).

Hence, using the formula, the variance comes out to be = 858.8623

So, standard deviation will be = sqrt(variance) = 29.30635

c. Diversification- "In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of assets." Basically what is meant by diversification is that instead of putting all your capital in one asset, you put it in varying types of assets so that the correlations between the performance of those assets reduce the risk of a big loss to the investor. For e.g. suppose you have invested in stocks. You come to know that the performance and return of gold have a negative correlation with stocks which means that when stocks go up, generally gold goes down and vice-versa. So, having gold also in your portfolio now will reduce the possibility of a huge loss to you as the losses in one asset will be compensated by the other.

d. False. Standard deviation can never be 0. Even if the portfolio always gives positive returns (profits), still there will be some standard deviation of the portfolio.