Arbor Systems and Gencore stocks both have a volatility of 33%. Compute the volatility of a portfolio with 50% invested in each stock if the correlation between the stocks is (a) +1.00, (b) 0.50, (c) 0.00, (d) −0.50, and (e) −1.00. In which of the cases is the volatility lower than that of the original stocks?

Explanation:

The formula to compute the volatility of a portfolio

Here,

The standard deviation of the first stock is σ₁

The standard deviation of the second stock is σ₂

The weight of the first stock W₁

The weight of the second stock W₂

The correlation between the stock c

a) If the correlation between the stock is +1

Hence, the volatility of the portfolio is 0.33 0r 33%

b) If the correlation between the stock is 0.50

Hence, the volatility of the portfolio is 0.29 0r 29%

c) If the correlation between the stock is 0.00

Hence, the volatility of the portfolio is 0.23 0r 23%

d) If the correlation between the stock is -0.50

Hence, the volatility of the portfolio is 0.17 or 17%

e) If the correlation between the stock is -1

Hence, the volatility of the portfolio is 0

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%