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The expected return is a crucial metric in financial risk assessment. It represents the average return that an investor anticipates from an investment over a future period. To calculate it, use the formula: \( \hat{k}_Y = \sum{(Probability \times Return)} \). This involves multiplying each possible return with its probability of occurring, then summing these products.
For example, in Stock Y, each potential return is weighted by its probability to get the expected value:

• For a 10% probability of 35% return, calculate 0.1 \( \times \) 0.35.
• For a 20% probability of 0% return, compute 0.2 \( \times \) 0.
• Continue similarly for other returns and probabilities.

The sum of these is 0.21, or 21%, which shows the expected annual return for Stock Y. Thus, expected return helps investors gauge the profit potential of their investments.

Standard deviation in finance measures the amount of variation or dispersion of a set of values. It reveals how much returns deviate from the expected return. A higher standard deviation signifies a higher risk in investments, as the returns are more spread out.
To determine the standard deviation for Stock X, first calculate the variance. This involves calculating each return's deviation from the mean, squaring it, multiplying by its probability, and summing up these values. The variance for Stock X is 0.11892. Taking the square root of variance gives the standard deviation, which is 0.3449 or 34.49% when expressed in percentage form.
This number helps investors understand the volatility, offering a clearer view of the risks associated with the stock's returns. If an investment has a high standard deviation, it implies more unpredictable returns, hence greater risk.

The coefficient of variation (CV) is a standardized measure of risk per unit of return, utilized when comparing the riskiness of investments with different expected returns. It is computed using the formula: \( CV_Y = \frac{\sigma_Y}{\hat{k}_Y} \), where \( \sigma_Y \) is the standard deviation and \( \hat{k}_Y \) is the expected return.
For Stock Y, the CV is calculated as \( \frac{0.2035}{0.21} \), yielding approximately 0.969, or 96.9%. This measure gives the proportion of the standard deviation relative to the expected return. A lower CV typically indicates a more favorable risk-return trade-off.
When compared with Stock X, Stock Y has a significantly lower CV, suggesting it has less risk in relation to its expected returns. For investors, this means that Stock Y, with its lower CV, might be perceived as less risky when considering how much return they can expect for each unit of risk taken.