Question

The expected return of a risky portfolio in New Zealand over 2022 is 15%, while the risk-free rate is 7%. Terry wishes to set up a complete portfolio, with y (the proportion invested in the risky portfolio) = 0.75.
REQUIRED:
1. Define a “complete portfolio”.
2. Describe the mix (or asset allocation) of Terry’s complete portfolio, including the percentages of each asset held.
3. What is the expected return of Terry’s complete portfolio?
4. What is the standard deviation of returns for Terry’s complete portfolio?
5. What is the Sharpe ratio for Terry’s complete portfolio?

Answer 1

1.

A complete portfolio is basically a portfolio which has a mix of risky and risk free asset. It is generally recommended for any investor to have a mix of various securities to diversify the risk and ensure a good and stable return.

 

2.

The mix is Risky asset as 75% of the complete portfolio and Risk free asset is 25% of the complete portfolio.

 

3.

Let's assume Risky assets as A and Risk free asset as B.

Expected return = (Weight of A*Return of A) + (Weight of B*Return of B)

                              = (75%*15) + (25%*7)

                             = 11.25 + 1.75

                             = 13%

 

4.

Standard deviation = √(Weight of A*Return of A) + (Weight of B*Return of B) +(2*Weight of A*Weight of B*Deviation of A*Deviation of B*Covariance of (A,B)

 

Covariance is a tool that help us to determine a relationship between two securities. A positive covariance means that if 1 security moves up the other security will also rise.

 

The covariance between a risky asset and a risk free asset is always 0. 

= √(0.75*15)+(0.25*7)+0    (as covariance is 0)

= √ 13

= 3.60%

 

5.

Sharpe Ratio = (Return of risky asset - Return for risk free return)/ Standard Deviation

                        = (15-7)/3.60

                       = 8/3.60

                       = 2.22 times.