Consider the following subjective probability distribution of returns on Stock X and Stock Y for a potential…

Question

Consider the following subjective probability distribution of returns on Stock X and Stock Y for a potential investment.

| State of economy | Probability | Estimated rate of returns | | :--- | :--- | :--- | :--- | | | | Stock X | Stock Y | | Strong growth | 0.10 | -10% | 20% | | Moderate growth | 0.40 | 5% | 15% | | Weak growth | 0.40 | 15% | 10% | | Recession | 0.10 | 30% | -10% |

a. Which stock would you select on the basis of expected return? b. Calculate standard deviation of the returns of Stock X and Stock Y, what purpose does standard deviation service for an investor? c. Calculate coefficient of variation for each stock. What purpose does coefficient of various serve? [3+5+2]

Padhai · Accepted Answer

Model Answer: Fundamentals of Investment (FIN253) – TU Board 2080 a. Expected Return and Stock Selection The expected return (E(R)) of a stock is calculated using the formula: E(R) = (P i R i) where: P i = Probability of each state of the economy R i = Return of the stock in that state Expected Return for Stock X E(R X) = (0.10 10\%) + (0.40 5\%) + (0.40 15\%) + (0.10 30\%) = ( 1\%) + (2\%) + (6\%) + (3\%) = 10\% Expected Return for Stock Y E(R Y) = (0.10 20\%) + (0.40 15\%) + (0.40 10\%) + (0.10 10\%) = (2\%) + (6\%) + (4\%) + ( 1\%) = 11\% Conclusion Since Stock Y (11%) has a higher expected return than Stock X (10%) , an investor seeking maximum expected return would select Stock Y . b. Standard Deviation of Returns The standard deviation (σ) measures the risk (volatility) of a stock’s returns. It is calculated as: = [P i (R i E(R))^2] Step 1: Calculate Variance for Stock X State of Economy Return (R) R E(R X) (R E(R X))^2 P i (R E(R X))^2 Strong Growth 10% 20% 400% 0.10 × 400% = 40% Moderate Growth 5% 5% 25% 0.40 × 25% = 10% Weak Growth 15% 5% 25% 0.40 × 25% = 10% Recession 30% 20% 400% 0.10 × 400% = 40% Total Variance 100% X = 100\% = 10\% Step 2: Calculate Variance for Stock Y State of Economy Return (R) R E(R Y) (R E(R Y))^2 P i (R E(R Y))^2 Strong Growth 20% 9% 81% 0.10 × 81% = 8.1% Moderate Growth 15% 4% 16% 0.40 × 16% = 6.4% Weak Growth 10% 1% 1% 0.40 × 1% = 0.4% Recession 10% 21% 441% 0.10 × 441% = 44.1% Total Variance 59% Y = 59\% 7.68\% Purpose of Standard Deviation Measures volatility (how much returns fluctuate). A higher standard deviation indicates higher risk . Investors use it to assess risk tolerance before selecting stocks. c. Coefficient of Variation (CV) The Coefficient of Variation (CV) is calculated as: CV = E(R) 100\% CV for Stock X CV X = 10\%10\% 100\% = 100\% CV for Stock Y CV Y = 7.68\%11\% 100\% 69.82\% Purpose of CV Compares risk adjusted returns between stocks. A lower CV means less risk per unit of return . Helps investors choose stocks with better risk return trade offs . Final Comparison Table Stock Expected Return Standard Deviation Coefficient of Variation (CV) X 10% 10% 100% Y 11% 7.68% 69.82% Interpretation: Stock Y has a higher expected return but lower risk (lower σ and CV). Stock X is riskier (higher CV) despite a lower return. Stock Y is the better choice for risk averse investors.

Consider the following subjective probability distribution of returns on Stock X and Stock Y for a potential investment. State of economy Probability Estimated rate of returns : : : : Stock X Stock…

Model Answer: Fundamentals of Investment (FIN253) – TU Board 2080

a. Expected Return and Stock Selection

Expected Return for Stock X

Expected Return for Stock Y

Conclusion

b. Standard Deviation of Returns

Step 1: Calculate Variance for Stock X

Step 2: Calculate Variance for Stock Y

Purpose of Standard Deviation

c. Coefficient of Variation (CV)

CV for Stock X

CV for Stock Y

Purpose of CV

Final Comparison Table

Discussion

More Fundamentals Of Investment questions

State of Economy	Return (R)	$R - E (R_{X})$	$(R - E (R_{X}))^{2}$	$P_{i} \times (R - E (R_{X}))^{2}$
Strong Growth	-10%	-20%	400%	0.10 × 400% = 40%
Moderate Growth	5%	-5%	25%	0.40 × 25% = 10%
Weak Growth	15%	5%	25%	0.40 × 25% = 10%
Recession	30%	20%	400%	0.10 × 400% = 40%
Total Variance				100%

State of Economy	Return (R)	$R - E (R_{Y})$	$(R - E (R_{Y}))^{2}$	$P_{i} \times (R - E (R_{Y}))^{2}$
Strong Growth	20%	9%	81%	0.10 × 81% = 8.1%
Moderate Growth	15%	4%	16%	0.40 × 16% = 6.4%
Weak Growth	10%	-1%	1%	0.40 × 1% = 0.4%
Recession	-10%	-21%	441%	0.10 × 441% = 44.1%
Total Variance				59%