# 16. Portfolio Performance Measurement and Evaluation

#### Parameters to define performance – risk and return-

When measuring and evaluating investment performance, it’s important to consider both the return earned and the associated risk. However, many people tend to focus solely on the return without taking into account the level of risk required to achieve that return. Therefore, a comprehensive performance measurement should include both return and risk assessment.

#### Rate of return measures-

Holding period return (HPR)-

Holding period return (HPR) is a simple and popular rate of return used to measure the performance of an investment. It calculates the income generated by an investment and the change in its value over the period it was held, expressed as a percentage per annum, relative to the beginning value of the investment.

For example, if an investor’s portfolio was valued at Rs.1,00,000 on 1 April, 2018, and on 31 March, 2019, the value was Rs.1,20,000, the HPR would be 20%, as calculated using Equation 1: HPR = (E-B)/B = ((120000-100000))/100000 = 20%.

If the investor also received Rs. 5000 by way of dividend and interest income during the same period, the HPR would be calculated using Equation 2: HPR = (I + (E -B)) / B = (5000 + (120000-100000))/100000 = 25%.

While this measure assumes that all income distributions are made at the end of the year, it is widely used and accepted as a starting point for performance measurement.

Time-Weighted Rate of Return (TWRR) and Money-Weighted Rate of Return (MWRR) are two ways to measure the rate of return over multiple holding periods. For instance, consider a portfolio that generated the following annual holding period return from 2015 through 2019:
-2015: -5.00%
-2016: -15.20%
-2017: 8.10%
-2018: 30.75%
-2019: 17.65%

Time Weighted Rate of Return (TWRR) versus Money Weighted Rate of Return (MWRR)-

Suppose further that an investor has invested Rs. 75,000 in this portfolio by making contributions at the beginning of the year. The portfolio value at the end of 2019 is Rs. 105,920.31.

To calculate the rate of return generated during the five-year period, we can use the internal rate of return (IRR) or MWRR. The IRR is calculated by discounting the terminal value of the investment to the cashflow contributions made. In this case, the IRR is 15.15%.

Alternatively, to calculate the underlying investment performance without being influenced by the timing of cash flows, we can use TWRR. TWRR is the compound rate of growth over the stated period. When there is an external cash flow, TWRR requires computing a set of returns for each period, which are then linked together to compute TWRR for the evaluation period.

In this example, there are five sub-periods, and the first step towards calculating the TWRR is to calculate each period return. The next step is to link these sub-period returns together using wealth relatives. Wealth relative is the ending value of one unit of money. We create a cumulative wealth relative for the entire evaluation period by multiplying each period wealth relative. The compound annual return can then be calculated as TWRR, which is 6.021%. Note that unless the sub-periods constitute exactly one year, TWRR will not be expressed as an annual rate, and we have to annualize the return.

Geometric Mean Return (GMR) vs. Arithmetic Mean Return (AMR)

Geometric Mean Return (GMR) and Arithmetic Mean Return (AMR) are two methods for calculating investment returns. To illustrate their differences, let’s consider two portfolio choices available for investment of Rs.100,000. The first choice produces a -50% return in the first year and a 100% return in the second year, while the second choice produces a 10% return in each of the two years.

At the end of the second year, the value of the portfolio for the first choice remains unchanged at Rs.100,000, resulting in an average annual return of 25%. Meanwhile, the value of the portfolio for the second choice increases to Rs.121,000, with an average annual return of 10%. Although the second choice has a lower AMR, it is still the better option.

AMR is the simple average of individual yearly returns, while GMR is 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 compounding. The GMR depends only on the initial and final values of the portfolio, not on the path by which that value was realized.

To calculate the GMR, we need to calculate wealth relatives for each holding-period rate of return, link these sub-period returns, and raise the cumulative wealth ratio to the power of 1/n, where n is the number of years. The GMR is always less than the AMR except when all the individual yearly returns are exactly the same.

The GMR is important for analyzing long-term returns on assets, while the AMR is a better estimate for a future year’s return based on the past year’s returns. While a fund manager can increase the average annual return by increasing risk, the GMR is the only way to compare long-term accumulations and understand what has really happened to investments. To estimate the probability distribution of terminal wealth, the GMR is the better option.

Gross versus net return

The gross return is the total return on an investment before any fees or expenses are deducted, and is usually stated for a specific period of time. The net return, on the other hand, is the return on an investment after all fees and expenses have been taken into account. This is the return that the investor actually receives.

It is important to consider both gross and net return when evaluating the performance of an investment. While gross return can provide a broad overview of how well an investment is performing, it can be misleading because it does not take into account any fees or expenses. Net return, on the other hand, provides a more accurate picture of the return an investor is actually earning.

To illustrate the difference between gross and net return, let’s look at an example of a portfolio. In this example, the size of the portfolio is Rs. 100 lacs, the investment period is one year, and the profit made during the year is 20% on the capital contribution. Other expenses such as brokerages and DP charges are charged on the gross value of the portfolio at 0.50%.

After taking into account all fees and expenses, the net return on this investment is 13.88%. This is lower than the gross return of 20%, but it provides a more accurate picture of the return an investor is actually earning.

Compounded Annual Growth Rate-

Compounded Annual Growth Rate (CAGR) is a measure of an investment’s annual growth rate over time, taking into account the effect of compounding. The calculation assumes that any dividends, income, or rent declared by the investment are reinvested in the same investment at the day’s market price.

The formula for calculating CAGR between the opening and closing wealth is (A/P)^(1/t)-1, where A is the closing wealth, P is the opening wealth, and t is the time period in years.

For example, if an investment of Rs. 100,000 is made in a certain investment for five years and the year-on-year returns are as follows: -5.00% in 2015, -15.20% in 2016, 8.10% in 2017, 30.75% in 2018, and 17.65% in 2019, the terminal wealth or the end-of-period value of the investment can be calculated.

Using the investment values at the end of each year as shown in the table, the CAGR can be calculated using the compound interest formula. In this case, the CAGR is 6.02%.

CAGR is a constant rate of growth required to reach the same terminal value over a given period of time. In the table, the investment value at the end of each year is shown along with the investment value at the end of the year growing at a rate of 6.02%.

Pre-tax versus post-tax return-

The pre-tax rate of return refers to the return on an investment before any taxes are paid, while the post-tax rate of return is the return after taxes have been paid on investment income and realized capital gains. Investors may belong to different tax brackets, so the performance of investments is communicated as the pre-tax rate of return. However, investors or their financial advisors need to calculate the post-tax return by adjusting the pre-tax return to the applicable tax rates.

The pre-tax return enables comparisons across different investments and strategies because different investors may be subject to different levels of taxation. However, what ultimately matters to the investor is the post-tax return. Therefore, investors make investment decisions based on post-tax performance.

An example of post-tax return calculation is provided below: Suppose an individual achieves a 5% pre-tax rate of return for stock XYZ and is subject to a capital gains tax of 15%. The post-tax rate of return would be calculated as follows:

Post-tax return = Pre-tax return x (1-tax rate)
Post-tax return = 5% x (1-15%) = 4.25%

Annualizing return-

Annualizing return is a method of calculating the compound average annual return of an investment in order to facilitate comparisons. To annualize a return, the chain linking method is used, and the product of the linking is raised to the reciprocal of the number of years in the evaluation period. For example, if a portfolio generated returns of 15.5% in 2017, 9.50% in 2018, and -6.90% in 2019, the first step in annualizing the return is to calculate the wealth relative. Then, the product of the wealth relative is taken and raised to the reciprocal of the number of years, and finally, 1 is subtracted from the result to obtain the annualized return.

It is important to note that annualizing a return for a period of less than a year is not advisable, as it involves extrapolating the return to a full year and may not accurately reflect the performance of the investment. This is particularly relevant for investments where returns can fluctuate significantly during the remaining period.

Cash drag adjusted return is a method of computing investment returns that takes into consideration the impact of uninvested cash on the overall portfolio return. When portfolio managers hold cash or other assets that are not invested in the portfolio, it can reduce the overall return of the portfolio. The cash drag adjusted return method adjusts for this by including the impact of the uninvested cash in the calculation of the portfolio return.

For example, if an investor has invested Rs. 100 lacs in an equity investment portfolio, but the manager has invested only Rs. 75 lacs in equities and Rs. 25 lacs are in liquid funds, the return on investment (ignoring the cash drag) would be calculated as 10% based on the Rs. 7.5 lacs return on the equities. However, adjusting for the cash drag, the return on investment would be calculated as (10% x Rs. 75 lacs) + (4% x Rs. 25 lacs) = Rs. 85,000 or 8.5% on Rs. 100 lacs.

By using the cash drag adjusted return method, investors can get a more accurate picture of the actual return on their investments, and portfolio managers can better evaluate the effectiveness of their investment strategies.

Alpha and beta-

In simple terms, alpha is a measure of a portfolio’s performance in excess of the expected return based on its beta, while beta is a measure of a portfolio’s sensitivity to market risk.

Alpha is a way to assess the value that a portfolio manager adds through their stock picking and market timing skills, above and beyond the overall market’s return. A positive alpha indicates that the portfolio has outperformed the market, while a negative alpha indicates underperformance.

Beta, on the other hand, measures how much the portfolio’s returns move in relation to the market as a whole. A beta of 1 indicates that the portfolio moves in lockstep with the market, while a beta greater than 1 indicates greater volatility than the market and a beta less than 1 indicates less volatility. A beta of 0 indicates no correlation with the market.

Portfolio Return-

The portfolio return is calculated as the weighted average return of individual securities in the portfolio. For example, if a portfolio consists of four securities with different weights and returns, the portfolio return can be calculated as follows:

Security A has a return of 15% and a weight of 30% in the portfolio.
Security B has a return of 10% and a weight of 20% in the portfolio.
Security C has a return of 12% and a weight of 20% in the portfolio.
Security D has a return of 18% and a weight of 30% in the portfolio.

The weighted average return of the securities in the portfolio is calculated by multiplying each security’s weight by its return and adding up the results. In this example, the portfolio return would be:

Portfolio Return = (15% x 30%) + (10% x 20%) + (12% x 20%) + (18% x 30%) = 14.30%

Therefore, the portfolio return for this example is 14.30%.

#### Risk Measures-

Risk is the possibility of loss, damage, or harm, and it is a crucial aspect of performance measurement and portfolio management. There are different definitions of risk for investments, but it is commonly defined as variability in the expected return or limited to losses or worse than expected outcomes only. Two measures of risk that have gained support in theory are the variance and the standard deviation of the estimated distribution of expected returns. However, downside risk, which includes concepts such as semi-variance/standard deviation and target semi-variance/standard deviations, is also relevant.

#### Performance Evaluation: Benchmarking and peer group analysis-

Performance evaluation is a crucial step in investment management, and it involves benchmarking and peer group analysis. A benchmark is a point of reference that serves as an objective test of the effective implementation of investment strategy. Popular choices for benchmarks include indices, and a good benchmark should meet several criteria such as being clearly defined, investable, consistent with the portfolio’s investment approach, having the same risk-return profile as the portfolio, and being measurable.

Sometimes market-based indices may not meet the criteria of a good benchmark, which calls for a customized benchmark that reflects the portfolio manager’s investment strategies and style. However, constructing and maintaining such benchmarks can be costly. Choosing the wrong benchmark or making benchmarking errors can lead to problems in evaluating portfolio performance accurately.

Peer group analysis is another popular way of evaluating portfolio performance. It involves comparing the performance of a portfolio to that of its peers with similar investment approaches and strategies. Portfolio tracking firms have developed databases to facilitate peer group analysis, ranking portfolios based on some risk-adjusted return measure.

Description:

1. Assets and Sector Allocation: This analysis determines the impact of the allocation of assets among various sectors on portfolio returns. It is measured against a benchmark to identify if over-investing in a specific economic sector resulted in differential returns.
2. Selection: This analysis measures the performance of the portfolio manager in selecting individual securities that outperform the benchmark. It examines the ability of the portfolio manager to identify securities that perform well relative to the benchmark.
3. Market Timing versus Selectivity: This analysis examines whether the performance of the portfolio was due to the timing of market movements or the ability to select profitable investments. It compares the portfolio manager’s ability to anticipate market movements against their ability to identify profitable investments.
4. Net Selectivity: This is an absolute measure of performance that takes into account the total risk of the portfolio. It calculates the annualized return of the fund, reduces it by the yield of a risk-free investment, and further reduces it by the standardized expected market premium times the total risk of the portfolio under review.
5. Local Currency versus Foreign Currency-Denominated Investment Return: This analysis calculates the return of foreign currency-denominated investments adjusted for fluctuations in the local currency against those foreign currencies. It determines whether currency fluctuations enhanced or reduced the return of the portfolio. This analysis is particularly relevant to investors who buy and sell securities denominated in currencies other than their local currency.

## Mock Test:-

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CHAPTER 16: PORTFOLIO PERFORMANCE MEASUREMENT AND EVALUATION .

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1. How can an investor analyze their financial position?

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2. What are hybrid portfolios primarily used for?

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3. What is the key difference between ethical investing and sustainable investing?

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4. What serves as a benchmark for evaluating the performance of a portfolio by comparing it with a similar composition portfolio?

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5. In Modern Portfolio Theory, investors estimate the risk of a portfolio based on

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6. According to Modern Portfolio Theory, investors want to maximize the return for a given level of

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7. What is the concept of the Efficient Frontier in portfolio optimization?

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8. How is stability in investment portfolios emphasized during the spending phase of the life cycle?

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9. How are investment objectives related to asset allocation decisions?

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10. What are the typical investment objectives of investors?

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11. What are some factors considered under governance in sustainable investing?

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12. What are investment constraints?

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13. What can be included in the Investment Policy Statement (IPS) regarding unique needs and preferences?

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14. Utility curves in Modern Portfolio Theory demonstrate

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15. How many correlation estimates are required for a portfolio of 50 securities?

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16. Risk averse investors in Modern Portfolio Theory prefer

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17. Why is portfolio rebalancing necessary?

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18. How does tax constraint impact investment decisions?

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19. How does sustainable investing impact investment decisions?

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20. What are the purposes served by an Investment Policy Statement (IPS)?

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21. True or False: Portfolio optimization using the MPT framework requires accurate estimation of statistical inputs.

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22. What falls under the category of liquidity constraints?

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24. Modern Portfolio Theory assumes that investors maximize

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25. What is the key factor that determines the selection of an optimum portfolio from feasible combinations?

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26. What is the difference between strategic asset allocation (SA and tactical asset allocation (TA?

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27. What does empirical evidence suggest about the importance of asset allocation?

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28. In portfolio optimization, what is the purpose of specifying investment constraints?

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29. What should be considered when preparing an Investment Policy Statement (IPS)?

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30. Which goals are considered near-term high priority goals?

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31. What does correlation measure?

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32. Which of the following statements is true regarding the Modern Portfolio Theory (MPT) framework?

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33. What phase of the life cycle of investing is characterized by income exceeding expenses?

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34. Which factor determines the extent of equity exposure in a portfolio?

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35. What is estimation risk in portfolio management?

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36. What is an example of a regulatory constraint?

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37. How does exposure to specific sectors, entities, and asset classes impact investment risk?

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38. The Certainty Equivalent Rate (CER) is the rate that a risk-free investment has to offer to be equally attractive with

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39. What is the calculation involved in portfolio risk comprising more than two securities?

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40. What is sustainable investing?

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41. What can exposure limits to different sectors, entities, and asset classes help mitigate?

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42. What role does psychographic analysis play in investor risk profile?

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43. How does correlation impact asset allocation decision?

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44. What are the steps involved in the portfolio construction process?

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45. What is the process of integrating investment objectives, goals, and requirements with capital market forecasts?

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46. Why is the selection of benchmarks crucial in evaluating portfolio performance?

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47. Risk-neutral investors evaluate investment opportunities solely based on

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48. When does the gifting phase of investing typically occur?

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49. What type of investments are usually preferred for near-term high priority goals?

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50. Why is it important to review and update the Investment Policy Statement (IPS) periodically?

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51. What is ethical investing?

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52. What should be considered while selecting debt instruments for a portfolio?

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53. What are the costs associated with portfolio rebalancing?

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54. What is the process of portfolio optimization?

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55. A risk-seeking investor in Modern Portfolio Theory is willing to engage in

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56. True or False: The portfolio variance formula considers the weighted averages of individual variances and covariances between assets in the portfolio.

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57. What is asset allocation in investment?

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58. What is the purpose of an Investment Policy Statement (IPS) in portfolio management?