Question

Review the example from the lecture about Umbrella Inc and Sunscreen Inc. Both companies have 10% return & 45% volatility and are perfectly negatively correlated.

•If an investor holds 50% in Umbrella Inc. & 50% in Sunscreen Inc.

•Expected return = 0.5(10%) + 0.5(10%) = 10%

•Expected risk = 0.5(45%) – 0.5(45%) = 0%

Owning both firms, investors can expect a 10% return “rain or shine”

a) What is the return and risk (volatility) of holding 100% in Umbrella Inc.?

b) Assume you sell 25% of Umbrella Inc and buy Sunscreen Inc. such that you hold 75% Umbrella and 25% Sunscreen. What is the return and risk of that portfolio?

c)  Now assume you sell another 25% of Umbrella and buy Sunscreen such that you now hold 50% of each stock. What is the return and risk of that portfolio?

d) Using the results from above, observe what happens to risk as you sell Umbrella (a 45% volatile stock) and buy Sunscreen (also a 45% volatile stock).

e) The risk of each stock (Sunscreen or Umbrella) by ITSELF is the its standard deviation, which is this example is 45%. What is the measure of each stock’s contribution to risk when held together in a portfolio? (Hint: the risk of a portfolio comprising equal proportions of Sunscreen & Umbrella is zero. Yet the risk of each stock by itself is 45%).

Answer 1

Portfolio return = Weight of stock 1 x Return of stock 1 + Weight of stock 2 x Return of stock 2

Portfolio risk = square root of [ (weight of stock1)2 (Standard deviation of stock1)2 + (weight of stock2)2 + (standard deviation of stock2)2 + 2(weight of stock 1)(weight of stock 2) (Correlation of two stocks)(Standard deviation of stock1)(standard deviation of stock2) ]

Standard deviation is equal to Volatility

a)

Holding 100% of Umbrella inc

Return = return of umbrella Inc = 10%

Risk = Volatility of Umbrella Inc = 45%

As only one stock exist in portfolio, the risk and return of such portfolio is equal to return and risk of that stock

b) Inserted picture

c) Inserted picture

d)

As we sell 25% stock of Umbrella and but Sunscreen stocks, the risk comes down from 22.49% to 0%. This is beacuse of the increase in the negatively correlated stock in the portfolio. This helps in reducing the overall risk of the portfolio as it is perfectly negatively correlated to the stock. Since both the stock are equally proportioned in portfolio, then the risk become zero.

e) The risk of both the stocks in the portfolio individually is 45% but when we invest in both of them simultaneously, the overall risk factor comes down as they are perfectly negatively correlated. Exactly at 50% each proportions, the risk will be zero. Any deviation from such proportion, the risk will increase constantly and reaches to 45% at either (100% of Umbrella and 0% of Sunscreen or 0% of Umbrella and 100% of Sunscreen)