Question

For the remaining questions, consider theses stocks and their historical return data. Assume that future return data will be similar to the historical data.

Stock	mu	sigma	rho A to B
A	12.0%	30.0%	-33.0%
B	13.0%	29.0%

1.What is the expected value return for a portfolio constructed of 50% A and 50% B? Round your answer to three decimal places.

2. What is the standard deviation of returns for a portfolio constructed of 50% A and 50% B? Round your answer to three decimal places and do not represent your answer as a percent.

3. Given your answers to the above two questions, would you prefer to invest in a) 100% stock B, or b) 50% stock A and 50% stock B? Answer a) or b) and provide a reason.

This option is the simplest to manage, the best average return, and has the lowest standard deviation

This option has the highest average return and a lower standard deviation than the other stock

This option has the best rho and a very good expected value return

b)

This option has the lowest standard deviation, the most diversification, and a decent expected-value return.

a)

4. An investor's mission is "to provide a portfolio of stocks that has positive returns, when market returns are positive or negative." This investor is:

A user of the CAPM model

A user of the Opportunity Investment Model

Beta focused

Alpha focused

Answer 1

We have been given :

Expected Returns:- E(R_A) = 12% , E(R_B) = 13%

Standard Deviation:- 30% ,   29% and

Correlation Coefficient:-    -33% i.e. -0.33

Weights:- W_A = 0.5 , W_B = 0.5

Q.1 Expected Return on the portfolio:- Expected return measures the mean, or expected value, of the probability distribution of investment returns. The expected return of a portfolio is calculated by multiplying the weight of each asset by its expected return and adding the values for each investment.

  

%

Therefore answer is 12.5%

Q.2 Standard Deviation of Returns on the portfolio:- the standard deviation of a portfolio measures how much the investment returns deviate from the mean of the probability distribution of investments.

Here:

= portfolio standard deviation

_WA = weight of asset A in the portfolio

_WB = weight of asset B in the portfolio

= standard deviation of asset A

= standard deviation of asset B; and

r_(a,b) = correlation of asset A and asset B

%

Therefore answer is 17.079%.

Q.3 Co-efficient of Variation is the meaure of risk taken to earn every unit of return. It is formulated by

  % i.e. 2.5 units of risk on return for every 1 unit of return

  % i.e. 2.23 units of risk on return for every 1 unit of return

% i.e. 1.37 units of risk on return for every 1 unit of return

Therefore:

Particulars	Stock A	Stock B	Portfolio A and B
Expected Returns	12%	13%	12.5%
Standard Deviation	30%	29%	17.079%
Coefficient of Variation	250%	223.08%	136.63%

We would like to invest in the Portfolio because it provides decent returns with the lowest standard deviation of returns i.e. risk. Portfolio in the combination of A and B has the negative rho therefore it provides most benefit of diversification i.e. risk got reduced and it also has the lowest CV.

✅ b).

✅ This option has the lowest standard deviation and most benefit of diversification, and a decent expected-value return

Q4. Answer for the question is Option C.) i.e. Beta Focused Investors

Explanation:

Correct Option C.) Beta Focused investors also called as the market timers believes that they can anticipate markets bullish or bearish trends with reasonable accuracy. Whenever market rises they increases beta of portfolio from low beta stocks to high beta stocks and vice versa. Therefore providing positive returns in both the situation where markets are positive and negative. Beta focused appproach combines both the advantages of passive investing and advantages of active investing strategies.

Incorrect Option A.) CAPM model based belives that markets are efficient. They invest in the diversified market portfolio to kill unsystematic risk. These investors replicates market benchmarks. Therefore their portfolio highly influenced by markets.

Incorrect option B.) Oportunity Investment Model based investors believes in fundamental analysis of stocks. They takes long position on underpriced stocks and short position on overpriced stocks.

Incorrect Option D.) Alpha focused strategies includes funds where stock selection, focused around identifying market winners, is based on research and analysis. They go long on underpriced stocks i.e. with positive alpha and go short on overprised stocks i.e. with negative alpha. These investors also holds undiversified portfolio.