Definition of Portfolio Evaluation

Portfolio manager evaluates his portfolio performance and identifies the sources of strength and weakness. The evaluation of the portfolio provides a feed back about the performance to evolve better management strategy. Even though evaluation of portfolio performance is considered to be the last stage of investment process, it is a continuous process. The managed portfolios are commonly known as mutual funds. Various managed portfolios are prevalent in the capital market. Their relative merits of return and risk criteria have to be evaluated.

Mutual Fund

Mutual fund is an investment vehicle that pools together funds from investors to purchase stocks, bonds or other securities. An investor can participate in the mutual fund by buying the units of the fund. Each unit is backed by a diversified pool of assets, where the funds have been invested. A closed-end fund has a fixed number of units outstanding. It is open for a specific period. During that period investors can buy it. The initial offer period is terminated at the end of the pre-determined period. The closed-end schemes are listed in the stock exchanges. The investor can trade the units in the stock markets just like other securities. The prices may be either quoted at a premium or discount.

In the open-end schemes, units are sold and bought continuously. The investors can directly approach the fund managers to buy or sell the units. The price of the unit is based on the net asset value of the particular scheme. The net asset value of the fund is the value of the underlying securities of the scheme. The net asset value is calculated on a daily or weekly basis.

The gain or loss made by the mutual fund is passed on to the investors after deducting the administrative expenses and investment management fees, The gains are distributed to the unit holder in the form of dividend or reinvested by the fund to generate further gains.

The mutual fund may be with or without a load factor. A commission or charge paid by the investors while purchasing or selling the mutual fund is known as load factor. Front-end load is charged when units are sold by the funds and back-end load is charged when the units are repurchased by the funds. The front-end load factor reduces the units when the investor buys it and the back-end load reduces the investor’s proceeds when he sells the units. Generally, the load factor ranges between 1 and 6 per cent of the net asset value. Sometimes, the fund may not charge both the loads.

Advantages of Mutual Funds

The Association of Mutual Funds in India (AMFI), a non- profit organization serving the cause of mutual funds, has listed the following advantages to the investors in mutual funds.

Professional Management

Experienced fund managers supported by a research team, select appropriate securities to the fund. The forecasting of the market is done effectively.

Diversification

Mutual funds invest in a diverse range of securities and over many industries. Hence, all the eggs are not placed in one basket. Normally an investor has to have large sum of money to achieve this objective, if he invests directly in the stock market. Through mutual funds, he can achieve diversification of portfolio at a fraction of the cost.

Convenient Administration

For the investors there is reduction in paper work and saving in time. It is also very convenient. Mutual funds help in overcoming the problems relating to bad deliveries, delayed payments and the like.

Return Potential

Medium and the long term mutual funds have the potential to provide high returns.

Low Costs

The funds handle the investments of a large number of people, they are in a position to pass on relatively low brokerage and other costs. This is because the funds can take advantage of the economies of scale.

Liquidity

Mutual funds’ provide liquidity in t ways. In open-end schemes, the investor can get back his money at any time by selling back the units to the fund at NAV related prices. In closed-end fund, he has the option to sell the units through the stock exchange.

Transparency

Mutual funds provide information on each scheme about the specific investments made there under and so on.

Flexibility

Currently most funds have regular investment plans, regular withdrawal plans and dividend reinvestment schemes. A great deal of flexibility is assured in the process.

Choice of Scheme

Mutual funds offer a variety of schemes to suit varying needs of the investors.

Well — Regulated

The funds are registered with the Securities and Exchange Board of India and their operations are continuously monitored.

Sharpe’s Performance Index

Sharpe’s performance index gives a single value to be used for the performance ranking of various funds or portfolios. Sharpe index measures the risk premium of the portfolio relative to the total amount of risk in the portfolio. This risk premium is the difference between the portfolio’s average rate of return and the riskless rate of return. The standard deviation of the portfolio indicates the risk. The index assigns the highest values to assets that have best risk-adjusted average rate of return

The details of two hypothetical funds A and B are given below

The larger the S. better the fund has performed. Thus, A ranked as better fund because its index .457> .427 even though the portfolio B had a higher return of 13.47 per cent. It is shown in Figure. The reason is that the fund ‘B’s managers took such a great risk to earn the higher returns and its risk adjusted return was not the most desirable. Sharpe index can be used to rank the desirability of funds or portfolios, but not the individual assets. The individual asset contains its diversifiable risk.

Treynor’s Performance Index

To understand the Treynor index, an investor should know the concept of characteristic line. The relationship between a given market return and the fund’s return is given by the characteristic line. The fund’s performance is measured in relation to the market performance. The ideal fund’s return rises at a faster rate than the general market performance when the market is moving upwards and its rate of return declines slowly than the market return, in the decline. The ideal fund may place its fund in the treasury bills or short sell the stock during the decline and earn positive return. The relationship between the ideal fund’s rate of return and the market’s rate of return is given by the figure

The market return is given on the horizontal axis and the fund’s rate of return on the vertical axis. When the market rate of return increases, the fund’s rate of return increases more than proportional and vice-versa. In the figure the fund’s rate of return is 20 per cent when the market’s rate of return is 10 per cent, and when the market return is —10, the fund’s return is 10 per cent. The relationship between the market return and fund’s return is assumed to be linear.

This linear relationship is shown by the characteristic line. Each fund establishes a performance relationship with the market. The characteristic line can be drawn by plotting the fund’s rate of return for a given period against the market’s return for the same period. The slope of the line reflects the volatility of the fund’s return.

A steep slope would indicate that the fund is very sensitive to the market performance. If the fund is not so sensitive then the slope would be a slope of less inclination.

All the funds have the same slope indicating same level of risk. The investor would prefer A fund, because it offers superior return than funds C and B for the same level of risk exposure. This is shown in (Figure)

With the help of the characteristic line Treynor measures the performance of the fund. The slope of the line is estimated by

Treynor’s risk premium of the portfolio is the difference between the average return and the riskless rate of return. The risk premium depends on the systematic risk assumed in a portfolio. Let us analyse to hypothetical funds.

Jensen’s Performance Index

The absolute risk adjusted return measure was developed by Michael Jensen and commonly known as Jensen’s measure. It is mentioned as a measure of absolute performance because a definite standard is set and against that the performance is measured. The standard is based on the manager’s predictive ability. Successful prediction of security price would enable the manger to earn higher returns than the ordinary investor expects to earn in a given level of risk.

The basic model of Jensen is given below

R_p  = α + ß (R_m – R_f)

R_p   = average return of portfolio

R_f   = riskless rate of interest

α    = the intercept

ß    = a measure of systematic risk

R_m = average market return

The return of the portfolio varies in the same proportion of 13 to the difference between the market return and riskless rate of interest. Beta is assumed to reflect the systematic risk. The fund’s portfolio beta would be equal to one if it takes a portfolio of all market securities. The 13 would be greater than one if the fund’s portfolio consists of securities that are riskier than a portfolio of all market securities. The figure shows the relationship between beta and fund’s return.

Any professional manager would be expected to earn average portfolio return of R = R1 + 1 (Rm_ Rf). If his predictive ability is superior, he should earn more than other funds at each level of risk. If the fund manager has consistently performed better than average Rp, there would be some constant factor that would make the actual return higher than average R. The constant may be that represents the forecasting ability of the manager. Then the equation becomes

R_p – R_f = α_p + ß (R_m – R_f)

Or

R_p = α_p + R_f + ß (R_m – R_f)

By estimating this equation with regression technique, Jensen claimed a the constant, reflected the professional management’s ability to forecast the price movements. A comparative analysis of three hypothetical funds A, B and C are given in the figure.

Fund A’s αp is equal to the risk free rate of return. If no risk is undertaken, the portfolio is expected to earn at least Rf. It is hypothesized that it takes no particular professional managerial ability to increase the return Rp by increasing (Rm – Rf). In the fund C, the manager’s predictive ability has made him earn more than Rf. The fund manager ‘would be consistently performing better than the fund A. At the same time if the profession management has not improved, it ‘would result in a negative a. This is shown by the line B. Here the is even below the riskless rate of interest. Jensen in his study of 115 funds, he found out that only 39 funds possessed positive a and employing professional management has improved the expected return. On an average, fund’s performance is worse than expected, without professional management and if any investor is to purchase fund’s shares, he must be very selective in his evaluation of management. Thus, Jensen’s evaluation of portfolio performance involves two steps.

Using the equation the expected return should be calculated.

With the help of 3, R_m and R,, he has to compare the actual return with the expected return. If the actual return is greater than the expected return, then the portfolio is considered to be functioning in a better manner. The following table gives the portfolio return and the market return. Rank the performance.

The return can be calculated with the given information using the formula:

R_p = R_f + ß (R_m – R_f)

Portfolio A = 5 + 1.2 (12-5) = 13.4

Portfolio B = 5 + 0.8 (12-5) = 10.6

Portfolio C = 5 + 1.5 (12-5) = 15.5

The difference between the actual and expected return is compared.

Portfolio A = 15—13.4= 1.6

Portfolio B = 12—10.6 = 1.4

Portfolio C =15—15.5 = -0.5:

Among the risk adjusted performance and of the three portfolios, A is the best, B - the second best and the last is the C portfolio.

Example

Mr. X has owned units from three different mutual funds namely R, S, and T. The following particulars are available to him. He wants to dispose any one of the mutual fund for his personal expenditure. Which fund should he dispose?

Ans: The performance can be evaluated by finding out the differential return. R - R = a + (R - R? (or)

R_p – R_f = α_p + ß (R_m – R_f)

Or

R_p = α_p + R_f + ß (R_m – R_f)

Portfolio R

α_p = (R_p - R_f) - ß_p (R_m – R_f)

 = 7.7— 1.02 x7.8 = -.256.

Portfolio S

α_p = 11.3 - .99 x 7.8

 = 3.578

Portfolio C

α_p = 11.6—1.07(7.8)

 = 3.254

Since the Portfolio R has a negative alpha value Mr. X can sell th portfolio R and keep the other

For ranking purpose, Jensen measure should be properly adjusted. Each asset’s alpha value should be divided by its beta co-efficient.