Risk-Adjusted Return Measures

This is everything you need to know about the Sharpe ratio: In the complex world of investment management, the Sharpe Ratio is a critical measure, enabling fund managers to assess the risk-adjusted return of their portfolios. What is the Sharpe Ratio? Developed by Nobel laureate William F. Sharpe, the Sharpe Ratio evaluates investment performance compared to a risk-free asset, adjusting for risk. It’s calculated by subtracting the risk-free rate from the investment return and dividing the result by the investment’s standard deviation. Why It Matters * Risk-Adjusted Returns: Provides a clear view of returns in relation to risk. * Performance Comparison: Helps compare the efficiency of different investments. * Investor Confidence: Reassures investors about fund management efficiency. How Does It Work? * Excess Return: Return of the investment minus the risk-free return. * Standard Deviation: Measures investment volatility or risk. * Ratio Calculation: Excess return divided by standard deviation. Interpreting the Sharpe Ratio * Good Ratios: Above 1.0: Good risk-adjusted returns. * Above 2.0: Very good, with significantly outweighing returns. * Above 3.0: Excellent, superior returns with low risk. * Bad Ratios:Below 1.0: Returns not compensating for risk. * Around 0: Returns only equal to the risk-free rate. * Negative: Underperforming the risk-free rate, indicating losses. Context Matters Economic environment and asset class are crucial. High-interest periods make high Sharpe Ratios challenging. Different asset classes have varying baseline expectations. Conclusion The Sharpe Ratio is vital for fund managers, helping them gauge and compare investment efficiency by considering both returns and risks. It underscores the importance of achieving high returns with a keen eye on risk, aligning investment strategies with investor objectives and risk tolerance.

One criticism of using standard deviation in the Sharpe ratio is that it takes into account deviations in both directions, both below and above the mean return. However, many investors are primarily concerned about downside risk, which refers to deviations below the mean return. To address this concern, a modification known as the Lower Partial Standard Deviation (LPSD) has been introduced. LPSD focuses solely on deviations below the mean return and is designed to mitigate the limitations of the traditional Sharpe ratio. Assuming you have a dataset of n returns and a risk-free rate (Rf), further assuming that m returns are less than this risk-free rate, the LPSD is defined as follows: LPSD = ∑(Ri - Rf)^2 / (m-1) where Ri < Rf The LPSD calculation is particularly useful in helping us compute the Sortino ratio. Similar to the Sharpe ratio, the Sortino ratio assesses risk-adjusted returns but exclusively considers the standard deviation of negative returns. This makes it a more suitable metric for investors who are more sensitive to potential losses, as it provides a refined measure of risk in their investment strategies.

You may know what ROC is, but have you come across 𝐑𝐀𝐑𝐎𝐂 yet?   𝐑𝐢𝐬𝐤-𝐀𝐝𝐣𝐮𝐬𝐭𝐞𝐝 𝐑𝐞𝐭𝐮𝐫𝐧 𝐨𝐧 𝐂𝐚𝐩𝐢𝐭𝐚𝐥 (𝐑𝐀𝐑𝐎𝐂) is a financial ratio that helps companies assess the return they’re generating on capital while factoring in the risks they’re taking   It’s crucial for understanding whether the returns justify the risks involved and is a powerful tool for comparing investments with varying risk levels   ↪ 𝐓𝐡𝐞 𝐅𝐨𝐫𝐦𝐮𝐥𝐚:   𝐑𝐀𝐑𝐎𝐂 = (r − e − el + ifc) / c   Where: 𝐫 = Revenue 𝐞 = Expenses 𝐞𝐥 = Expected loss (average loss over a specified period) 𝐢𝐟𝐜 = Income from capital (capital charges × the risk-free rate) 𝐜 = Capital   𝐂𝐨𝐧𝐬𝐢𝐝𝐞𝐫, 𝐂𝐨𝐦𝐩𝐚𝐧𝐲 𝐁 - invests ₹10 crore in a high-risk startup   ↪ 𝐀𝐬𝐬𝐮𝐦𝐩𝐭𝐢𝐨𝐧𝐬: Revenue (r) = ₹1.5 crore Expenses (e) = ₹0.3 crore Expected Loss (el) = ₹0.8 crore (25% potential loss) Income from Capital (ifc) = ₹0.4 crore Capital (c) = ₹10 crore   Now, let’s calculate the RAROC for Company B: RAROC = (1.5 − 0.3 − 0.8 + 0.4) / 10  𝐑𝐀𝐑𝐎𝐂 = 0.08 or 8%   ↪ 𝐖𝐡𝐚𝐭 𝐝𝐨𝐞𝐬 𝐭𝐡𝐢𝐬 𝐦𝐞𝐚𝐧? Company B’s investment yields a risk-adjusted return of 8%, which tells us that after accounting for all costs, losses, and capital charges, the return on this investment is modest but positive #return #capital LinkedIn

Value can only be added on a risk-adjusted basis. Alpha = return relative to beta Sharpe = return relative to std. deviation Calmar = return relative to drawdown Sortino = return relative to downside deviation The most reliable way of improving all of these ratios is by including independent sources of return in your portfolio (aka diversifying well). Without diversification, you are relying on security selection to beat a benchmark, which is notoriously difficult and unreliable. Independent sources of returns are hard to come by at the asset class level. This is why I prefer liquid alternatives, which can be structurally setup to be negatively correlated to equities. Either way, if you are not allocating risk to one of the following asset classes or alternative strategies, I can almost guarantee that you have little-to-no diversification against the systematic risk of equities, and are therefore not adding value for your clients: - Long duration U.S. Treasuries - Oil/Energy - Gold - Long/Short Equity - Managed Futures - Systematic Global Macro