Question

a) “The standard deviation of a portfolio's return cannot be reduced to zero by holding all the securities in the market.” True or false? Explain. (2 mark)

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 30%
• $35 with a probability of 60%
• $23 with a probability of 10%

b) Calculate the expected return for holding the share for a year. (2 mark)

c) Calculate the variance of return and standard deviation of return.

d) On December 1, 2020, the share is worth $36 and the investor just received a dividend of $2.50. Calculate the total holding period return and capital gains return over the one-year period.

e) Explain the difference between expected return and realised return.

Answer 1

Ans: a) “The standard deviation of a portfolio's return cannot be reduced to zero by holding all the securities in the market.

TRUE: Standard Deviation measures the volatility of Return for any stock/portfolio. Now if we keep on adding stock in our portfolio its Standard Deviation will keep reducing. But after a certain limit, Standard deviation will stagnant. It will reciprocate with market volatility. So we can not reduce to zero of the portfolio's e standard deviation by holding all the securities in the market.

• Return = ( Expected Price in Each Scenario - Current Price) / Current Price

= ( Expected Price in Each Scenario - 50 ) / 50

• Cumulative Return = Probability * Return in each condition
• Expected Return = Sum of Cumulative Return
• Price Deviation from Expected return = Expected Return - Return in each condition
• Square Return Deviation from Expected return = (Price Deviation from Expected return ) 2
• Weighted Square Price Deviation from Expected return = Probability * Square Price Deviation from Expected return in each condition
• Variance = Sum of Weighted Square Price Deviation from Expected return
• Standard Deviation = Sqrt of Variance

b) the expected return for holding the share for a year. = 19.69% (Ans)

c) the variance of return and standard deviation of return. (Ans)

Variance	6.93%
Standard Deviation	26.33%

d) On December 1, 2020, the share is worth $36 and the investor just received a dividend of $2.50.

Holding Period Return =

= 20.31%

capital gains return =

= (36 - 32) / 32

= 4 /32

= 12.5%

Holding Period Return = 20.31% (Ans)

capital gains return = 12.5% (Ans)

e) the difference between expected return and realised return.

Expected Returns are future projection of stock price based on different economic / business scenario. Where realised return are actual return.