📘 16.1 Performance Evaluation Overview
What is Performance Evaluation?
Performance evaluation is the process of assessing how well a portfolio has performed. It involves comparing the portfolio’s returns against appropriate benchmarks or peer group standards. The goal is to measure the effectiveness of the portfolio manager in achieving the investment objectives while managing risk.
Why is Performance Evaluation Important?
Assessing Portfolio Success
Performance evaluation allows investors to understand how their investments are performing relative to market conditions, similar portfolios, and benchmarks. By evaluating performance, investors can identify whether the portfolio manager has added value or whether the returns are merely a result of passive market movements.
Steps in the Performance Evaluation Process
1. Set Benchmarks
The first step in performance evaluation is to set **benchmarks**. Benchmarks are used as reference points to compare portfolio performance. A suitable benchmark reflects the type of assets and investment strategy of the portfolio.
2. Calculate Portfolio Returns
The next step is to calculate the **returns** generated by the portfolio. This includes all income and capital gains, taking into account fees and other costs.
3. Compare Returns with Benchmark
The portfolio’s returns are then compared with the **benchmark** returns to assess the relative performance. This helps determine if the portfolio outperformed or underperformed the benchmark.
4. Adjust for Risk
Risk-adjusted returns are then calculated. This helps to understand if higher returns were due to higher risks or if the manager achieved above-average returns for the same level of risk.
📘 16.2 Rate of Return Measures
What is Rate of Return?
Rate of return (RoR) is a critical metric for measuring the performance of a portfolio. It quantifies the profit or loss on an investment over a certain period. There are several ways to calculate return depending on the investment type and the goals of the investor. The rate of return can help an investor determine whether a portfolio is meeting its investment objectives.
16.2.1 Holding Period Return
What is Holding Period Return?
The holding-period return (HPR), also known as the total return or point-to-point return, measures the return on an investment over the period it is held. It includes the income generated by the investment (like dividends) and the change in the asset’s value during that period.
For example, if the market value of an investor’s portfolio on 1st April, 2018, is Rs. 1,00,000, and on 31st March, 2019, the value of the portfolio stands at Rs. 1,20,000, the holding-period return would be 20%. This can be calculated using the formula:
HPR = (Ending Value – Beginning Value) / Beginning Value
Example calculation:
HPR = (120000 - 100000) / 100000 = 20%
If the investor received Rs. 5,000 by way of dividends, the calculation changes to:
HPR = (5000 + (120000 - 100000)) / 100000 = 25%
16.2.2 Time Weighted Rate of Return (TWRR) vs Money Weighted Rate of Return (MWRR)
What is TWRR?
Time-weighted rate of return (TWRR) calculates the return on an investment by removing the impact of external cash flows (like additional investments or withdrawals). This is useful when assessing the performance of a fund or portfolio manager, as it evaluates the portfolio’s ability to generate returns without considering the timing of cash inflows and outflows.
What is MWRR?
Money-weighted rate of return (MWRR) is similar to the internal rate of return (IRR) and considers the timing and amount of cash flows. It is useful for evaluating the returns that an investor would earn based on their own contribution and the portfolio’s performance. The MWRR is particularly useful when cash flows are irregular or occur at different times.
To calculate MWRR, we use the cash flow method and find the discount rate that sets the present value of cash flows equal to the final portfolio value.
16.2.3 Geometric Mean Return (GMR) vs Arithmetic Mean Return (AMR)
What is Geometric Mean Return (GMR)?
Geometric mean return is the compound annual growth rate (CAGR) of an investment, assuming that dividends or income are reinvested. It reflects the true annualized return of an investment over time, factoring in the effects of compounding. It is especially useful when analyzing the long-term return of an asset or portfolio.
What is Arithmetic Mean Return (AMR)?
Arithmetic mean return is the simple average of the yearly returns. It adds up all the individual returns and divides by the number of periods. While easy to compute, it is not as accurate for multi-period returns, as it does not account for the compounding effect.
For example, if an investment had a return of -50% in year 1 and 100% in year 2, the arithmetic average return would be 25%, which can be misleading. The geometric return, in this case, would be 0%, giving a more accurate depiction of performance.
16.2.4 Gross vs Net Return
What is Gross Return?
**Gross return** is the total return generated by an investment before any deductions for fees, expenses, or commissions. It provides an initial measure of an investment’s performance. However, focusing on gross return can be misleading, as it doesn’t reflect the true earnings of the investor.
What is Net Return?
**Net return** is the return after accounting for all costs associated with the investment, such as management fees, taxes, and other expenses. It represents the actual return the investor earns after all deductions. Net return is crucial for assessing the real profitability of an investment.
16.2.5 Pre-tax vs Post-tax Return
What is Pre-tax Return?
**Pre-tax return** is the return before accounting for taxes. It is used to compare investments and assess their performance before any tax obligations are considered.
What is Post-tax Return?
**Post-tax return** is the return after accounting for taxes. Investors are usually more concerned with post-tax return, as it reflects the actual earnings that will be available to them after paying taxes on dividends, capital gains, and other investment income.
16.2.6 Compounded Annual Growth Rate (CAGR)
What is CAGR?
**CAGR** is the measure of an investment’s annual growth rate over a specified period of time, with compounding. It calculates the consistent rate of growth, assuming that dividends and gains are reinvested into the investment at the end of each period. The formula for CAGR is:
CAGR = (Ending Value / Beginning Value) ^ (1 / Time Period) - 1
For example, if an investment grows from Rs. 100,000 to Rs. 133,960 over 5 years, the CAGR is:
CAGR = (133960 / 100000) ^ (1 / 5) - 1 = 6.02%
16.2.7 Annualizing Return
What is Annualized Return?
**Annualized return** represents the average annual return over a specified period, adjusted for compounding. It gives a clearer picture of long-term investment performance by converting periodic returns into a single annual figure. Annualizing the return helps to compare investments with different time horizons.
16.2.8 Cash Drag Adjusted Return
What is Cash Drag?
**Cash drag** refers to the impact on a portfolio’s return caused by holding a large portion of the investment in cash or cash equivalents. Although cash provides liquidity, it tends to earn a lower return, which can reduce the overall portfolio performance. Cash drag is especially important when calculating the return on an investment portfolio where not all capital is actively invested.
16.2.9 Alpha and Beta Return
What is Alpha Return?
**Alpha** is the excess return generated by a portfolio above its benchmark index, after adjusting for risk. It measures the portfolio manager’s ability to outperform the market or a particular asset class.
What is Beta Return?
**Beta** measures the risk of a portfolio in relation to the market. A Beta greater than 1 indicates that the portfolio is more volatile than the market, while a Beta less than 1 indicates lower volatility. Beta is used to evaluate systematic risk and is often used in the **Capital Asset Pricing Model (CAPM)** to calculate the expected return of a portfolio.
📘 16.3 Risk Measures
What is Risk?
Risk refers to the possibility of losing or damaging an investment. It is the key factor in determining the potential return of an investment. Risk helps investors make decisions that align with their tolerance for potential loss. Understanding the different types of risks is crucial for constructing a well-balanced portfolio.
16.3.1 Total Risk and Downside Risk
What is Total Risk?
Total risk refers to the variability of returns, or the degree to which returns can fluctuate. It includes both upside and downside movements in an investment’s value. The higher the total risk, the greater the potential for variation in returns.
What is Downside Risk?
Downside risk focuses specifically on the possibility of loss or negative returns. It only considers the risk of underperforming relative to expectations, rather than the overall volatility of returns.
Two common measures of risk used are standard deviation (total risk) and semi-variance (downside risk).
16.3.2 Portfolio Risk vs Individual Risk
What is Portfolio Risk?
Portfolio risk is the overall risk of a portfolio, which takes into account not only the risks of the individual assets within it but also how these assets interact with one another. It considers both the weights of the investments and the correlations between them. The risk of the entire portfolio may be lower than the sum of the individual risks, especially if the assets are not perfectly correlated.
What is Individual Risk?
Individual risk refers to the risk associated with a single asset. This risk is usually measured by the asset’s standard deviation, which quantifies how much the asset’s returns deviate from the average return.
16.3.3 Market Risk
What is Market Risk?
Market risk is the risk that the entire market or a particular segment of the market will experience significant fluctuations, affecting all securities within that segment. Factors such as interest rates, inflation, and global events can influence market risk. Market risk cannot be diversified away, but it can be hedged using various strategies.
16.3.4 Interpreting Volatility
Standard Deviation as a Measure of Total Risk
Standard deviation is a statistical measure that quantifies the degree to which a security’s or portfolio’s returns deviate from the average. A higher standard deviation means higher risk, as it indicates that returns are more spread out and less predictable.
Standard deviation is one of the most commonly used tools to measure risk in finance, helping to assess the variability of returns and the potential for large fluctuations in price.
Semi-Variance as a Measure of Downside Risk
Semi-variance measures the dispersion of returns only below the mean, identifying the downside risk of an investment. Unlike standard deviation, which accounts for both positive and negative deviations, semi-variance focuses only on negative returns.
Although semi-variance is useful for understanding downside risk, it is less popular in practice due to the difficulty of accurately forecasting asymmetrical distributions of returns.
16.3.5 Tracking Error
What is Tracking Error?
Tracking error is the standard deviation of the difference between the returns of a portfolio and its benchmark. It is used to assess how closely the portfolio follows its benchmark index. A lower tracking error indicates that the portfolio’s returns are more closely aligned with the benchmark’s returns.
Tracking error helps in evaluating the performance consistency of the portfolio manager. If the portfolio’s returns deviate too much from the benchmark, it may indicate that the manager is taking more risk than necessary.
16.3.6 Systematic Risk and Unsystematic Risk
What is Systematic Risk?
Systematic risk refers to the risk that affects the entire market or large segments of the market, such as economic events or changes in government policy. Systematic risk cannot be eliminated through diversification. It is typically measured by Beta, which reflects the sensitivity of an asset’s returns to overall market movements.
What is Unsystematic Risk?
Unsystematic risk is risk that is unique to an individual asset or company, such as management changes, product recalls, or legal issues. This risk can be reduced through diversification, as it does not affect the entire market.
16.3.7 Beta
What is Beta?
Beta is a measure of a security’s or portfolio’s sensitivity to market movements. It indicates how much the security’s price is expected to change in relation to changes in the broader market index. A beta of 1 means that the security will move in line with the market, while a beta greater than 1 indicates higher volatility, and a beta less than 1 indicates lower volatility.
16.3.8 Liquidity Risk
What is Liquidity Risk?
Liquidity risk refers to the risk that an asset cannot be quickly converted into cash at its fair market value. Liquid assets, like treasury bills or stocks of large companies, have low liquidity risk, while illiquid assets like real estate or collectibles can be harder to sell without incurring a loss.
16.3.9 Credit Risk
What is Credit Risk?
Credit risk is the risk that a borrower will default on their debt obligations. This is especially relevant for debt securities, where the risk of the issuer failing to make payments can affect the returns on the investment.
📘 16.4 Risk-adjusted Return Measures
What are Risk-adjusted Return Measures?
Risk-adjusted return measures help in evaluating a portfolio’s performance based on its returns relative to the amount of risk taken. These measures allow investors to assess the performance of different investments by adjusting for the level of risk involved. Popular risk-adjusted return measures include Sharpe ratio, Treynor ratio, Sortino ratio, and more.
16.4.1 Sharpe Ratio
What is Sharpe Ratio?
The Sharpe Ratio measures a portfolio’s excess return over the risk-free return, divided by the portfolio’s standard deviation (risk). This ratio shows how much return the investor is getting for each unit of risk they take on. A higher Sharpe ratio indicates better risk-adjusted returns.
Formula:
Sharpe Ratio (S) = (Rp – Rf) / σp
Where:
Rp = Return of the portfolio
Rf = Risk-free return
σp = Standard deviation of the portfolio’s return.
Example: If the annualized return for a portfolio is 10.50%, the risk-free rate is 5.50%, and the standard deviation is 6.50%, the Sharpe ratio is:
Sharpe Ratio = (10.50% – 5.50%) / 6.50% = 0.7692
This suggests that the portfolio generated 0.7692 percentage points of return for each unit of risk.
16.4.2 The Treynor Ratio
What is the Treynor Ratio?
The Treynor Ratio measures a portfolio’s excess return relative to its systematic risk (beta). It is calculated by dividing the portfolio’s excess return over the risk-free rate by its beta. The Treynor ratio focuses on the reward for taking market risk.
Formula:
Treynor Ratio (T) = (Rp – Rf) / βp
Where:
Rp = Portfolio return
Rf = Risk-free return
βp = Portfolio beta
Example: If the portfolio’s return is 10.50%, the risk-free rate is 5.50%, and the portfolio’s beta is 1, the Treynor ratio would be:
Treynor Ratio = (10.50% – 5.50%) / 1 = 0.05
This means the portfolio earned 0.05 percentage points for each unit of market risk.
16.4.3 Sharpe vs Treynor Measure
Sharpe vs Treynor
The main difference between the Sharpe and Treynor ratios is the measure of risk they use. The Sharpe ratio uses total risk (standard deviation), whereas the Treynor ratio uses systematic risk (beta). For a well-diversified portfolio, the results from both ratios will often align. However, for poorly diversified portfolios, Treynor may provide a higher ranking since it ignores unsystematic risk.
Sharpe Ratio: Best for portfolios with significant unsystematic risk.
Treynor Ratio: More useful for well-diversified portfolios where unsystematic risk is minimal.
16.4.4 Sortino Ratio
What is Sortino Ratio?
The Sortino Ratio is similar to the Sharpe ratio but it only considers the downside risk (semi-standard deviation) rather than the total risk. This ratio is useful for investors who view risk as the possibility of losing money rather than just volatility.
Formula:
Sortino Ratio = (Rp – Rf) / Semi-Standard Deviation of Portfolio
A higher Sortino ratio indicates a better risk-adjusted return, especially when the investor is more concerned with losses than volatility.
16.4.5 Information Ratio (Appraisal Ratio)
What is the Information Ratio?
The Information Ratio (IR) measures the consistency of a portfolio’s excess return relative to a benchmark. It helps determine whether a portfolio’s alpha is a result of skill or luck. A higher IR suggests that the fund manager is consistently generating excess returns over the benchmark with less risk.
Formula:
IR = (Rp – Rb) / Stdev(Rp – Rb)
Where:
Rp = Portfolio return
Rb = Benchmark return
Stdev(Rp – Rb) = Standard deviation of the differences between the portfolio and benchmark returns.
16.4.6 Modigliani and Modigliani Ratio (M2)
What is the Modigliani and Modigliani (M2) Ratio?
The Modigliani and Modigliani (M2) ratio adjusts a portfolio’s risk to match the risk of the market portfolio. By adjusting for market risk, the M2 ratio provides a direct comparison of a portfolio’s return with the market’s return.
Formula:
M2 = (Portfolio Return * Weight of Portfolio) + (Risk-Free Return * Weight of Risk-Free Asset)
Example: If the portfolio’s return is 35%, the market return is 28%, and the portfolio’s standard deviation is 42%, while the market’s standard deviation is 30%, the M2 can be computed to compare the adjusted return with the market.
📘 16.5 Performance Evaluation: Benchmarking and Peer Group Analysis
What is Performance Evaluation?
Performance evaluation is a critical process that helps to assess how well a portfolio manager has performed compared to relevant benchmarks or similar portfolios. It helps investors understand if the portfolio manager has generated returns above passive strategies and whether the fees charged are justified.
16.5.1 Characteristics of Indices for Benchmarking
🔍 Clear Definition
A good benchmark must have clearly defined constituents and their respective weights. It should be measurable and representative of the portfolio being evaluated.
📈 Investable Benchmark
The benchmark must be investable, meaning it’s possible to have a passive exposure to the benchmark itself. This ensures that the performance of the portfolio is truly comparable.
🎯 Consistency with Portfolio’s Strategy
The benchmark should align with the portfolio’s investment strategy. For example, if the portfolio invests in blue-chip stocks, the benchmark should also consist of blue-chip stocks.
⚖️ Matching Risk-Return Profile
The benchmark must have the same risk-return profile as the portfolio. A mismatch in risk levels would distort the comparison between portfolio and benchmark performance.
16.5.2 Customized Benchmark
When is a Customized Benchmark Needed?
Sometimes, market-based indices may not represent the investment strategy and style of the portfolio. In such cases, portfolio managers create customized benchmarks by selecting attractive securities from a specific investment universe. These benchmarks cater to specific needs but are more costly to construct and maintain compared to market-based indices.
16.5.3 Benchmarking Errors
Common Benchmarking Errors
Common errors include selecting a benchmark that doesn’t align with the portfolio’s strategy or changing the portfolio’s style without updating the benchmark. Additionally, benchmarks that are hard to invest in, have volatile components, or lack proper data may lead to inaccurate comparisons.
16.5.4 Managers’ Universe Analysis
What is Managers’ Universe Analysis?
Managers’ universe or peer group analysis compares a portfolio’s performance with that of similar portfolios. By ranking portfolios with similar risk-return profiles, it helps investors assess how their portfolio is performing relative to others in the same category. This method uses risk-adjusted return measures to evaluate performance accurately.
📘 16.6 Performance Attribution Analysis
What is Performance Attribution?
Performance attribution is the process of analyzing the sources of returns in a portfolio to understand what factors contributed to its performance. It helps investors assess whether the return was due to the portfolio manager’s skill or just random factors (luck). The main focus is on two components: return driven by the benchmark and differential return.
16.6.1 Assets and Sector Allocation
🔑 Overweighting Winning Sectors
Differential return can be achieved by being overweight in sectors that outperform the benchmark or underweight in sectors that underperform.
📊 Allocation Effect
The allocation effect calculates the difference based on the allocation and return generated by each sector. Understanding trends in the economy and sectors is key to beating the benchmark.
16.6.2 Selection
Choosing the Right Securities
Differential return can be earned by selecting securities that perform well relative to the benchmark or avoiding securities that perform poorly. Picking winners and avoiding losers boosts portfolio performance.
16.6.3 Market Timing vs Selectivity
Market Timing
Market timing involves anticipating market movements and investing to take advantage of them. However, studies show that market timing is less effective than stock selection for generating superior returns.
Selectivity
Selectivity refers to choosing securities that outperform the market. While results are mixed, selectivity can enhance returns if the right securities are chosen.
16.6.4 Net Selectivity
What is Net Selectivity?
Net selectivity measures the absolute performance of a portfolio by comparing it to the risk-free return and adjusting for the portfolio’s total risk. It quantifies the excess return earned by the manager beyond what could have been earned by investing in the market portfolio.
16.6.5 Local Currency vs Foreign Currency Denominated Investment Return
Currency Risk
When investing in foreign-denominated assets, currency fluctuations affect the return. The risk comes from the change in value between the local currency (INR) and the foreign currency (USD in this example).
Example: Indian Investor in US Equity Fund
An investor invests Rs. 50 lacs in a US equity fund. The value grows by 15%, but the Indian rupee appreciates from Rs. 70/$ to Rs. 65/$. The return in INR terms becomes only 6.79% instead of 15% due to the INR appreciation.
