PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION

PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION (Part 1)

• Parameters to define performance:
  • Risk: The uncertainty or volatility of investment returns.
  • Return: The profit or loss earned by an investment over a certain period.
• Calculating Return:
  • Holding Period Return (HPR): The total return earned by an investment over a specific period, including income and capital gains.
  • Time Weighted Rate of Return (TWRR): The compound rate of growth over a stated period, unaffected by the timing of cash flows.
  • Money Weighted Rate of Return (MWRR): The annual rate of return at which cumulative contributions grow over the measurement period, influenced by the timing of cash flows.
• Calculating Risk:
  • Volatility: The degree of uncertainty or fluctuation in investment returns.
  • Standard Deviation: A measure of the dispersion of investment returns from their mean value.
• Calculating Risk-Adjusted Return:
  • Sharpe Ratio: A measure of the excess return earned by an investment over the risk-free rate, relative to its volatility.
  • Treynor Ratio: A measure of the excess return earned by an investment over the risk-free rate, relative to its systematic risk.
• Importance of Benchmarking and Peer Group Analysis:
  • Benchmarking: The process of comparing an investment's performance to a standard or reference point.
  • Peer Group Analysis: The process of comparing an investment's performance to that of similar investments or peer groups.
• Performance Attribution Analysis:
  • Attribution Analysis: The process of analyzing an investment's performance to determine the sources of its returns, such as asset allocation, security selection, or other factors.

Key Concepts

• Holding Period Return (HPR): Calculated using the formula HPR = (E-B)/B, where E is the ending value, B is the beginning value, and I is the income earned during the period.
• Time Weighted Rate of Return (TWRR): Calculated by linking sub-period returns together, using the formula TWRR = (1 + r)^n - 1, where r is the sub-period return and n is the number of sub-periods.
• Money Weighted Rate of Return (MWRR): Calculated using the formula MWRR = (FV / PV)^(1/n) - 1, where FV is the future value, PV is the present value, and n is the number of periods.
• Geometric Mean Return (GMR): A measure of the average return over multiple periods, calculated using the formula GMR = (1 + r1) * (1 + r2) * ... * (1 + rn)^(1/n) - 1, where r is the return for each period and n is the number of periods.
• Arithmetic Mean Return (AMR): A measure of the average return over multiple periods, calculated using the formula AMR = (r1 + r2 + ... + rn) / n, where r is the return for each period and n is the number of periods.

PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION (Part 2)

• Geometric Mean Return (GMR): The rate at which the sum invested at the beginning of the period will accumulate to a given sum at the end of the period by the process of compounding, or continuously reinvesting dividends and capital gains.
• Characteristics of GMR:
  • Depends only on the initial and final values of the portfolio, not on the path by which that value was realized.
  • Based on an exponential function, which represents periodic compounding.
  • Calculated by linking sub-period returns.
• Gross Return vs Net Return:
  • Gross Return: The total return generated on investment before the deduction of any fees, expenses, or commissions.
  • Net Return: The return earned after adjusting for fees, expenses, or commissions.
• Pre-tax Return vs Post-tax Return:
  • Pre-tax Return: Returns before taxes.
  • Post-tax Return: Returns after taxes are paid on investment income and realized capital gains.
  • Formula: Post-tax return = Pre-tax return x (1 - tax rate)
• Compounded Annual Growth Rate (CAGR):
  • A measure of an investment's annual growth rate over time, with compounding.
  • Formula: (A / P)^(1 / t) - 1, where A is the closing wealth, P is the opening wealth, and t is the time period in years.
• Annualizing Return:
  • The process of reporting the rate of return on an annualized basis.
  • Formula: Same as CAGR or geometric mean return.
• Cash Drag Adjusted Return:
  • The return on investment adjusted for the cash component in the portfolio.
  • Importance: Accurately reflects the return on the entire portfolio, including cash.
• Alpha and Beta Return:
  • Alpha: The return generated by a portfolio over the required rate of return as per the Capital Asset Pricing Model (CAPM).
  • Beta: A measure of market risk, or the systematic risk of a portfolio.
  • Formula: Portfolio Return - Rf + B (Rm - Rf) = Alpha Return, where Rf is the risk-free return, B is the market beta, and Rm is the return on a market portfolio.

PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION (Part 3)

• Alpha Return: Reward for bearing non-market risk, also referred to as Jensen alpha.
• Beta Return: Reward for bearing market risk.
• Excess Return: Return over the market benchmark return, calculated as the difference between the portfolio return and the market benchmark return.

Portfolio Return

• Definition: The weighted average return of individual securities in the portfolio.
• Calculation: Portfolio Return = (Return of Security A * Weight of Security A) + (Return of Security B * Weight of Security B) + ... + (Return of Security N * Weight of Security N).

Risk Measures

• Total Risk: Variability in the expected return, measured by variance or standard deviation.
• Downside Risk: Losses or worse than expected outcomes, measured by semi-variance or semi-standard deviation.
• Portfolio Risk: Depends on the weights of the investments, their individual standard deviations, and the correlation across those investments.
• Covariance: A product of the coefficient of correlation between the assets' returns and their individual standard deviations.

Types of Risk

• Market Risk: Arises due to fluctuations in the prices of equity shares due to various market-related dynamics, measured by Beta.
• Systematic Risk: Risk due to common risk factors, such as interest rates, exchange rates, and commodities prices, measured by Beta.
• Unsystematic Risk: Risk due to sector-specific or company-specific factors, which can be diversified away.
• Liquidity Risk: Uncertainty introduced by the secondary market of an investment, defined as the ease of converting an asset into cash at close to its economic worth.
• Credit Risk: Risk that the borrower is not able to repay the amounts on time to the lender, arising in case of debt instruments.

Risk-Adjusted Return Measures

• Sharpe Ratio: Measures reward to variability, calculated as the excess return of the portfolio over the risk-free return, divided by the portfolio's standard deviation.
• Treynor Ratio: Adjusts excess return for systematic risk, calculated as the excess return of the portfolio over the risk-free return, divided by the portfolio's beta.
• Tracking Error: Standard deviation of the difference between the portfolio and its target benchmark portfolio total return.
• Tracking Difference: Simple point-to-point difference between index return and fund return.

PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION (Part 4)

• Introduction: To evaluate a portfolio's performance, investors need to consider various measures that take into account the level of diversification and the type of risk involved.
• Sharpe versus Treynor Measure:
  • Sharpe Ratio: Uses standard deviation of return as the measure of risk.
  • Treynor Ratio: Uses Beta (systematic risk) as the measure of risk.
  • Key Difference: For a well-diversified portfolio, both measures give identical rankings, but for a poorly diversified portfolio, the Treynor Ratio may give a higher ranking as it ignores unsystematic risk.

Performance Measurement Ratios

• Sortino Ratio:
  • Definition: Portfolio’s return in excess of the risk-free return divided by the portfolio’s semi-standard deviation.
  • Purpose: Adjusts portfolio’s excess return to the downside risk, making it appealing to investors who view risk as the chance of losing money.
• Information Ratio (Appraisal Ratio):
  • Formula: (Rp – Rb)/Stdev (p-b), where Rp is the return on the portfolio, Rb is the return on the benchmark, and Stdev (p-b) is the standard deviation of the observations of differences between the return of the portfolio and return of the benchmark.
  • Purpose: Determines whether an observed alpha is due to skill or chance.
• Modigliani and Modigliani Ratio (M2) Measure:
  • Definition: Adjusts the risk of the portfolio to match the risk of the market portfolio.
  • Purpose: Allows for a direct comparison of returns between the portfolio and the market portfolio.

Performance Evaluation

• Benchmarking:
  • Definition: Evaluating a portfolio's performance against a suitable benchmark or similar portfolios.
  • Purpose: Enables investors to determine if the portfolio manager has enhanced the portfolio's value beyond what could be obtained from a passive indexed strategy.
• Peer Group Analysis:
  • Definition: Evaluating a portfolio's performance against a group of similar portfolios.
  • Purpose: Provides a yardstick to evaluate the performance of the portfolio and determine if the portfolio management fees are justified.

Characteristics of Indices for Benchmarking

• Good Benchmark: Should be representative of the portfolio, investable, consistent with the portfolio's investment approach, and have the same risk-return profile as the portfolio.
• Customized Benchmark: May be necessary when market-based indices do not meet the criteria of a good benchmark.

Performance Attribution Analysis

• Definition: Analyzing what drives the performance and the reasons behind it.
• Purpose: Enables investors to take further investment decisions.
• Components: Return driven by the benchmark and the differential return.
• Asset and Sector Allocation:
  • Definition: Choosing to over-invest in or under-invest in a particular economic sector or asset category.
  • Purpose: Can lead to differential return and better performance.
• Selection:
  • Definition: Selecting securities that perform well relative to the benchmark or avoiding benchmark securities that perform poorly.
  • Purpose: Can lead to differential return and better performance.
• Market Timing versus Selectivity:
  • Definition: Market timing is the ability to anticipate developments in the market, while selectivity is the ability to select securities that generate extra returns.
  • Purpose: Both can lead to better performance, but most studies show that market timing is not the primary factor.

PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION (Part 5)

• Portfolio Return: The return earned by a fund manager, reduced by the standardized expected market premium times the total risk of the portfolio under review, showing the excess return that cannot be earned by investing in the market portfolio.
• Currency Risk: The risk associated with investments denominated in foreign currencies, where fluctuations in currency values can either enhance or reduce returns.
• Local Currency vs. Foreign Currency Denominated Investment Return: An Indian investor needs to calculate the return after adjusting for the fluctuation in Indian rupee against foreign currencies, as the return earned on investments denominated in foreign currencies would not be the same when converted back to rupee term.

Key Concepts

• Return Calculation: The return earned on investments denominated in foreign currencies needs to be calculated after adjusting for currency fluctuations.
• Currency Appreciation/Depreciation: The appreciation or depreciation of the Indian rupee against foreign currencies can either reduce or enhance the returns associated with foreign investments.
• Example: An Indian investor invests in a US equity fund, and the return earned is 15%. However, due to the appreciation of the Indian rupee, the return in rupee term is approximately 6.79%, which is lower than the expected return.

Sample Questions

• Portfolio Risk: If the correlation coefficient between two stocks decreases over time, the portfolio's risk would decrease.
• Efficient Portfolio: The envelope curve containing the set of best possible combinations is known as the Efficient portfolio.
• Sustainable Investing: Sustainable investing considers all of the above, including social, environmental, and governance factors.
• Rebalancing Portfolio: Rebalancing the portfolio should be done at regular intervals.
• Sharpe's Performance Measure: Sharpe's performance measure divides the portfolio's risk premium by the standard deviation of the rate of return.