A 10-year research on 3 distinct portfolios and the market reveals the following information: | Portfolio | Average Annual Return | Standard Deviation | Beta | |-----------|------------------------|--------------------|------| | 1 | 14% | 21 | 1.15 | | 2 | 16% | 24 | 1.00 | | 3 | 20% | 28 | 1.25 | | S&P 500 | 12% | 20 | — | Given that the risk-free rate of return is 6%, use the Sharpe measure to rank the portfolios from the lowest to the highest. | Financial Risk Manager Part 1 Quiz

A 10-year research on 3 distinct portfolios and the market reveals the following information:

Portfolio	Average Annual Return	Standard Deviation	Beta
1	14%	21	1.15
2	16%	24	1.00
3	20%	28	1.25
S&P 500	12%	20	—

Given that the risk-free rate of return is 6%, use the Sharpe measure to rank the portfolios from the lowest to the highest.

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TTanishq

Explanation:

Explanation

The Sharpe ratio is calculated using the formula:

$S_p = \frac{E(R_p) - R_f}{\sigma_p}$

Where:

$E(R_p)$ = Expected portfolio return
$R_f$ = Risk-free rate (6%)
$\sigma_p$ = Portfolio standard deviation

Let's calculate the Sharpe ratios for each portfolio:

Portfolio 1: $S_1 = \frac{14\% - 6\%}{21} = \frac{8\%}{21} = 0.3809$

Portfolio 2: $S_2 = \frac{16\% - 6\%}{24} = \frac{10\%}{24} = 0.4167$

Portfolio 3: $S_3 = \frac{20\% - 6\%}{28} = \frac{14\%}{28} = 0.5000$

Ranking from lowest to highest Sharpe ratio:

Portfolio 1: 0.3809
Portfolio 2: 0.4167
Portfolio 3: 0.5000

Therefore, the correct ranking from lowest to highest is 1, 2, 3, which corresponds to option D.

Note: The beta values and S&P 500 information are not needed for Sharpe ratio calculations, as Sharpe ratio uses total risk (standard deviation) rather than systematic risk (beta).

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