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8/3/2019 Answers SAPM

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Q 1

Performance Measures Of

Mutual Funds


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Performance Measures Of Mutual

Funds Return alone should not be considered as the basis ofmeasurement of the performance of a mutual fund scheme, itshould also include the risk taken by the fund manager becausedifferent funds will have different levels of risk attached to them.

Risk associated with a fund, in a general, can be defined as

variability or fluctuations in the returns generated by it. The higher the fluctuations in the returns of a fund during a given

period, higher will be the risk associated with it. These fluctuationsin the returns generated by a fund are resultant of two guidingforces.

First, general market fluctuations, which affect all the securitiespresent in the market, called market risk or systematic risk

Second, fluctuations due to specific securities present in the portfolioof the fund, called unsystematic risk


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Mutual fund performance must be evaluated on a risk-to-

return basis, as neither risk or return alone is provides a

sufficient means of evaluation..

The coefficient of variation (CV) is a fund's standard deviation

divided by its return. This gives you a risk-to-return ratio, i.e.,units of risk per unit of return, that can be used to compare

mutual fund performance on a level basis.

CV = si ri

Where:

si = thestandard deviation of asset i

ri =the mean return of asset i


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The Total Risk of a given fund is sum of these two and is measuredin terms of

Standard deviation of returns of the fund.

Systematic risk, on the other hand, is measured in terms ofBeta,which represents fluctuations in the NAV of the fund.

The more responsive the NAV of a mutual fund is to the changes inthe market; higher will be its beta. Beta is calculated by relating thereturns on a mutual fund with the returns in the market.

While unsystematic risk can be diversified through investments in anumber of instruments, systematic risk can not. By using the risk

return relationship, we try to assess the competitive strength of themutual funds vis-a-vis one another in a better way.


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The most important and widely used

measures of performance are:

The Treynor Measure

The Sharpe Measure

Jenson Model


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The Treynor Measure Developed by Jack Treynor

This performance measure evaluates funds on the basis of Treynor's Index.This Index is a ratio of return generated by the fund over and above risk

free rate of return (generally taken to be the return on securities backed by

the government, as there is no credit risk associated), during a given period

and systematic risk associated with it (beta). Symbolically, it can be

represented as:

Treynor's Index (Ti) = (Ri - Rf)/Bi.

Where, Ri represents return on fund, Rfis risk free rate of return and Biisbeta of the fund.

All risk-averse investors would like to maximize this value. While a high andpositive Treynor's Index shows a superior risk-adjusted performance of a

fund, a low and negative Treynor's Index is an indication of unfavorable

performance.


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The Sharpe Measure

In this model, performance of a fund is evaluated on thebasis of Sharpe Ratio,

It is a ratio of returns generated by the fund over and aboverisk free rate of return and the total risk associated with it.

It is the total risk of the fund that the investors are

concerned about. So, the model evaluates funds on thebasis of reward per unit of total risk. Symbolically, it can bewritten as:

Sharpe Index (Si) = (Ri - Rf)/Si

Where, Si is standard deviation of the fund.

While a high and positive Sharpe Ratio shows a superiorrisk-adjusted performance of a fund, a low and negativeSharpe Ratio is an indication of unfavorable performance.


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Comparison of Sharpe and Treynor

Sharpe and Treynor measures are similar in a way, since they both dividethe risk premium by a numerical risk measure.

The total risk is appropriate when we are evaluating the risk return

relationship for well-diversified portfolios. On the other hand, the

systematic risk is the relevant measure of risk when we are evaluating less

than fully diversified portfolios or individual stocks. For a well-diversified portfolio the total risk is equal to systematic risk.

Rankings based on total risk (Sharpe measure) and systematic risk (Treynor

measure) should be identical for a well-diversified portfolio, as the total

risk is reduced to systematic risk.

Therefore, a poorly diversified fund that ranks higher on Treynor measure,compared with another fund that is highly diversified, will rank lower on

Sharpe Measure.


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Jenson Model Jenson's model proposes another risk adjusted performance

measure.

This measure was developed by Michael Jenson and is sometimesreferred to as the Differential Return Method.

This measure involves evaluation of the returns that the fund hasgenerated vs. the returns actually expected out of the fund giventhe level of its systematic risk.

The surplus between the two returns is called Alpha, whichmeasures the performance of a fund compared with the actualreturns over the period.

Jensen's alpha = Portfolio Return *Risk Free Rate Portfolio Beta (Market Return Risk Free Rate)+

Higher alpha represents superior performance of the fund and viceversa.

Limitation of this model is that it considers only systematic risk notthe entire risk associated with the fund


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Treynor measure and Jenson model usesystematic risk based on the premise that theunsystematic risk is diversifiable.

These models are suitable for large investorslike institutional investors with high risk takingcapacities as they do not face paucity of fundsand can invest in a number of options to dilutesome risks. For them, a portfolio can bespread across a number of stocks and sectors.


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5 Ways To Measure Mutual Fund

Risk

There are five main indicators of investment riskthat apply to the analysis of stocks, bonds andmutual fund portfolios. They are alpha, beta, r-

squared, standard deviation and the Sharpe ratio. All of these risk measurements are intended to

help investors determine the risk-rewardparameters of their investments. In this article,

we'll give a brief explanation of each of thesecommonly used indicators.


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Alpha

Alpha is a measure of an investment's performance on arisk-adjusted basis. It takes the volatility (price risk) of asecurity or fund portfolio and compares its risk-adjustedperformance to a benchmark index. The excess return ofthe investment relative to the return of the benchmarkindex is its "alpha.

Alpha is often considered to represent the value that aportfolio manager adds or subtracts from a fund portfolio'sreturn. A positive alpha of 1.0 means the fund hasoutperformed its benchmark index by 1%. Correspondingly,a similar negative alpha would indicate anunderperformance of 1%. For investors, the more positivean alpha is, the better it is.


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Beta

Beta, also known as the "beta coefficient," is a measure of the volatility, or

systematic risk, of a security or a portfolio in comparison to the market as

a whole. Beta is calculated using regression analysis, and you can think of

it as the tendency of an investment's return to respond to swings in the

market. By definition, the market has a beta of 1.0. Individual security and

portfolio values are measured according to how they deviate from the

market. A beta of 1.0 indicates that the investment's price will move in lock-step

with the market. A beta of less than 1.0 indicates that the investment will

be less volatile than the market, and, correspondingly, a beta of more than

1.0 indicates that the investment's price will be more volatile than the

market. For example, if a fund portfolio's beta is 1.2, it's theoretically 20%more volatile than the market.

Conservative investors looking to preserve capital should focus on

securities and fund portfolios with low betas, whereas those investors

willing to take on more risk in search of higher returns should look for high

beta investments.


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R-Squared

R-Squared is a statistical measure that represents thepercentage of a fund portfolio's or security's movementsthat can be explained by movements in a benchmark index.

For fixed-income securities and their corresponding mutualfunds, the benchmark is the Treasury Bill and, likewise withequities and equity funds, the benchmark is the Nifty Index.

R-squared values range from 0 to 100, a mutual fund withan R-squared value between 85 and 100 has a performancerecord that is closely correlated to the index. A fund rated70 or less would not perform like the index.


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Standard Deviation

Standard deviation measures the dispersion ofdata from its mean. The more that data is spreadapart, the higher the difference is from the norm.In finance, standard deviation is applied to the

annual rate of return of an investment tomeasure its volatility (risk). A volatile stock wouldhave a high standard deviation. With mutualfunds, the standard deviation tells us how much

the return on a fund is deviating from theexpected returns based on its historicalperformance.

Q 3


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Copyright 2005 Pearson

Addison-Wesley. All rights

reserved.

5-17

Components of Risk

Diversifiable (Unsystematic) Risk

Results from uncontrollable or random events that arefirm-specific

Can be eliminated through diversification

Examples: labor strikes, lawsuits

Nondiversifiable (Systematic) Risk

Attributable to forces that affect all similar investments

Cannot be eliminated through diversification Examples: war, inflation, political events


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reserved.

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Components of Risk

Total risk Nondiversifiable risk Diversifiable risk


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reserved.

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Beta: A Popular Measure of Risk

A measure of nondiversifiable risk

Indicates how the price of a security responds tomarket forces

Compares historical return of an investment to the marketreturn (the S&P 500 Index)

The beta for the market is 1.00

Stocks may have positive or negative betas. Nearly all arepositive.

Stocks with betas greater than 1.00 are more risky than the

overall market. Stocks with betas less than 1.00 are less risky than the overall

market.


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reserved.

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Beta: A Popular Measure of Risk


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reserved.

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Interpreting Beta

Higher stock betas should result in higher expectedreturns due to greater risk

If the market is expected to increase 10%, a stock

with a beta of 1.50 is expected to increase 15% If the market went down 8%, then a stock with a

beta of 0.50 should only decrease by about 4%

Beta values for specific stocks can be obtained fromValue Line reports or online websites suchas yahoo.com


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reserved.

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Interpreting Beta

Stock Beta Stock BetaAmazon.com 1.60 Intl Business

Machines1.10

Anheuser Busch 0.60 Merrill Lynch & Co. 1.60Bank of America

Corp.

1.25 Microsoft 1.15

Dow Jones & Co. 1.00 Nike, Inc. 0.90Disney 1.25 PepsiCo, Inc. 0.65eBay 1.55 Qualcomm 1.20Exxo nMobil Corp. 0.80 Sempra Energy 0.85Gap (The), Inc. 1.35 Wal-Mart Stores 1.00General Motors Corp. 1.20 Xerox 1.45

Intel 1.35 Yahoo! Inc. 1.85


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Q4


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Definition of Efficient Markets

An efficient capital market is a market that is efficient inprocessing information.

We are talking about an informationally efficient market, asopposed to a transactionally efficient market. In other

words, we mean that the market quickly and correctly adjuststo new information.

In an informationally efficient market, the prices of securitiesobserved at any time are based on correct evaluation of allinformation available at that time.

Therefore, in an efficient market, prices immediately and fullyreflect available information.

Q4


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Definition of Efficient Markets (cont.)

Professor Eugene Fama, who coined the phrase efficient

markets, defined market efficiency as follows:

"In an efficient market, competition among the many intelligent

participants leads to a situation where, at any point in time, actual

prices of individual securities already reflect the effects of informationbased both on events that have already occurred and on events which,

as of now, the market expects to take place in the future. In other

words, in an efficient market at any point in time the actual price of a

security will be a good estimate of its intrinsic value."


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The Efficient Markets Hypothesis

The Efficient Markets Hypothesis (EMH) is

made up of three progressively stronger

forms:

Weak Form

Semi-strong Form

Strong Form


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The EMH Graphically

In this diagram, the circles

represent the amount of

information that each form of

the EMH includes.

Note that the weak form

covers the least amount of

information, and the strong

form covers all information.

Also note that each successiveform includes the previous

ones.

Strong Form

Semi-Strong

Weak Form

All information, public and privateAll public information

All historical prices and returns


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The Weak Form

The weak form of the EMH says that past prices, volume, and othermarket statistics provide no information that can be used to predict futureprices.

If stock price changes are random, then past prices cannot be used toforecast future prices.

Price changes should be random because it is information that drivesthese changes, and information arrives randomly.

Prices should change very quickly and to the correct level when newinformation arrives (see next slide).

This form of the EMH, if correct, repudiates technical analysis.

Most research supports the notion that the markets are weak formefficient.


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Price Adjustment with New

Information

At 10AM EST, the U.S. Supreme Court refused to hear an appeal from

MSFT regarding its anti-trust case. The stock immediately dropped. This

example, one of hundreds available every day, illustrates that prices adjust

extremely rapidly to new information.But, did the price adjust correctly? Only time will tell, but it does seem

that over the next hour the market is searching for the correct level.

Notes: Each bar represents high, low, and close for one-minute. Each solid gridline represents the top of an hour, and each dotted

gridline represents a half-hour.


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Tests of the Weak Form

Serial correlations.

Runs tests.

Filter rules. Relative strength tests.

Many studies have been done, and nearly all

support weak form efficiency, though therehave been a few anomalous results.


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The Semi-strong Form

The semi-strong form says that prices fully reflect all publiclyavailable information and expectations about the future.

This suggests that prices adjust very rapidly to newinformation, and that old information cannot be used to earn

superior returns. The semi-strong form, if correct, repudiates fundamental

analysis.

Most studies find that the markets are reasonably efficient inthis sense, but the evidence is somewhat mixed.


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Tests of the Semi-strong Form

Event Studies

Stock splits

Earnings announcements

Analysts recommendations

Cross-Sectional Return Prediction

Firm size

BV/MV

P/E


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The Strong Form

The strong form says that prices fully reflect all

information, whether publicly available or not.

Even the knowledge of material, non-public

information cannot be used to earn superior

results.

Most studies have found that the markets are

not efficient in this sense.


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Tests of the Strong Form

Corporate Insiders.

Specialists.

Mutual Funds.

Studies have shown that insiders andspecialists often earn excessive profits, butmutual funds (and other professionally

managed funds) do not. In fact, in most years, around 85% of all

mutual funds underperform the market.


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reserved.

5-37

Two Approaches

to Constructing Portfolios

Traditional Approach

versus

Modern Portfolio Theory

Q 6


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Traditional Approach

Emphasizes balancing the portfolio using a widevariety of stocks and/or bonds

Uses a broad range of industries to diversify

the portfolio

Tends to focus on well-known companies Perceived as less risky

Stocks are more more liquid and available

Familiarity provides higher comfort levelsfor investors


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Addison-Wesley. All rightsreserved.

5-39

Modern Portfolio Theory (MPT)

Emphasizes statistical measures to develop aportfolio plan

Focus is on:

Expected returns Standard deviation of returns

Correlation between returns

Combines securities that have negative (or low-

positive) correlations between each others ratesof return


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Key Aspects of MPT:

Efficient Frontier

Efficient Frontier

The leftmost boundary of the feasible set of portfolios thatinclude all efficient portfolios: those providing the bestattainable tradeoff between risk and return

Portfolios that fall to the right of the efficient frontier arenot desirable because their risk return tradeoffsare inferior

Portfolios that fall to the left of the efficient frontier arenot available for investments


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5-41

Figure 5.7 The Feasible or Attainable Set and

the Efficient Frontier


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MARKET STRUCTURE

(JULY 31, 2005) 22 Stock Exchanges,

Over 10000 Electronic Terminals at over 400 locations all over India.

9108 Stock Brokers and 14582 Sub brokers

9644 Listed Companies

2 Depositories and 483 Depository Participants

128 Merchant Bankers, 59 Underwriters

34 Debenture Trustees, 96 Portfolio Managers

83 Registrars & Transfer Agents, 59 Bankers to Issue

4 Credit Rating Agencies

Q 7

I di C i l M k


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Indian Capital Market

Market Instruments Intermediaries

Primary Secondary

Equity DebtHybrid

Regulator

Brokers

Investment Bankers

Stock ExchangesUnderwriters

SEBI

Players

Corporate IntermediariesCRA Banks/FI FDI /FIIIndividual


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The role of the stock exchange

Raising capital for businesses

Mobilizing savings for investment

Facilitate company growth

Redistribution of wealth


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The role of the stock exchange

Corporate governance

Creates investment opportunities for small investors

Government raises capital for development projects

Barometer of the economy


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Capital Market Instruments

ADR / GDR

Equity Debt

EquityShares

PreferenceShares

Debentures Zero couponbonds

DeepDiscount

Bonds

Hybrid


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5-48

Capital Asset Pricing Model (CAPM)

Model that links the notions of riskand return

Helps investors define the required return on

an investment

As beta increases, the required return for agiven investment increases


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Capital Asset

Pricing Model (CAPM) (contd)

Uses beta, the risk-free rate and the marketreturn to define the required return onan investment

Required return

on investmentj Risk-free rate

Beta for

investmentj

Market

return

Risk-free

rate

Q 8


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5-51

Capital Asset

Pricing Model (CAPM) (contd)

CAPM can also be shown as a graph

Security Market Line (SML) is the picture ofthe CAPM

Find the SML by calculating the requiredreturn for a number of betas, then plottingthem on a graph


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Risk, Return and PortfolioTheory

Measuring ReturnsIntroduction

Ex Ante Returns

Return calculations may be done before-the-fact, in which case, assumptions must be

made about the future

Ex Post Returns

Return calculations done after-the-fact, inorder to analyze what rate of return wasearned.

Q 9


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Measuring Average ReturnsEx Post Returns

Measurement of historical rates of return thathave been earned on a security or a class ofsecurities allows us to identify trends ortendencies that may be useful in predictingthe future.

There are two different types of ex post mean

or average returns used: Arithmetic average

Geometric mean


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CHAPTER 8 Risk, Returnand Portfolio Theory 8 - 55

Measuring Average ReturnsArithmetic Average

Where:

ri= the individual returns

n = the total number of observations

Most commonly used value in statistics Sum of all returns divided by the total number of observations

(AM)AverageArithmetic 1

n

rn

i

i

[8-4]


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Measuring Average ReturnsGeometric Mean

Measures the average or compound growthrate over multiple periods.

11111(GM)MeanGeometric1

321 -)]r)...(r)(r)(r[(n

n[8-5]


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Measuring Average ReturnsGeometric Mean versus Arithmetic Average

If all returns (values) are identical the geometric mean = arithmetic

average.

If the return values are volatile the geometric mean < arithmeticaverage

The greater the volatility of returns, the greater the difference

between geometric mean and arithmetic average.

(Table 8 2 illustrates this principle on major asset classes 1938 2005)


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Measuring Average ReturnsAverage Investment Returns and Standard Deviations

Annual

Arithmetic

Average (%)

Annual

Geometric

Mean (%)

Standard Deviation

of Annual Returns

(%)

Government of Canada treasury bills 5.20 5.11 4.32

Government of Canada bonds 6.62 6.24 9.32

Canadian stocks 11.79 10.60 16.22

U.S. stocks 13.15 11.76 17.54

Source: Data are from the Canadian Institute of A ctuaries

Table 8 - 2 Average Investment Returns and Standard Deviations, 1938-2005

The greater the difference, the

greater the volatility of annual

returns.


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Measuring Expected (Ex Ante) Returns

While past returns might be interesting,investors are most concerned with futurereturns.

Sometimes, historical average returns will not berealized in the future.

Developing an independent estimate of ex ante

returns usually involves use of forecastingdiscrete scenarios with outcomes andprobabilities of occurrence.


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Estimating Expected ReturnsEstimating Ex Ante (Forecast) Returns

The general formula

Where:

ER = the expected return on an investment

Ri= the estimated return in scenario i

Probi= the probability of state i occurring

)Prob((ER)ReturnExpected1

i n

i

ir[8-6]

E i i E d R


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Estimating Expected ReturnsEstimating Ex Ante (Forecast) Returns

Example:

This is type of forecast data that are required to make an ex

ante estimate of expected return.

State of the Economy

Probability of

Occurrence

Possible

Returns on

Stock A in that

State

Economic Expansion 25.0% 30%

Normal Economy 50.0% 12%Recession 25.0% -25%

Estimating Expected Returns


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Estimating Expected ReturnsEstimating Ex Ante (Forecast) Returns Using a Spreadsheet

Approach

Example Solution:

Sum the products of the probabilities and possible returns in

each state of the economy.

(1) (2) (3) (4)=(2)(1)

State of the Economy

Probability of

Occurrence

Possible

Returns on

Stock A in that

State

Weighted

Possible

Returns on

the StockEconomic Expansion 25.0% 30% 7.50%

Normal Economy 50.0% 12% 6.00%Recession 25.0% -25% -6.25%

Expected Return on the Stock = 7.25%

E ti ti E t d R t


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Estimating Expected ReturnsEstimating Ex Ante (Forecast) Returns Using a Formula Approach

Example Solution:

Sum the products of the probabilities and possible returns in

each state of the economy.

7.25%)25.0(-25%0.5)(12%.25)0(30%

)Prob(r)Prob(r)Prob(r

)Prob((ER)ReturnExpected

332211

1

i

n

i

ir


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Active or Passive Management?

Investors, as a group, can do no better than the market,because collectively they are the market. Most investors trail the marketbecause they are burdened by commissions and fund expenses. Jonathan Clements, the Wall Street Journal,June 17, 1997

Fees paid for active management are not a good deal for investors, andthey are beginning to realize it. Michael Kostoff, executive director, TheAdvisory Board, a Washington-based market research firm.InvestmentNews, February 8, 1999

When you layer on big fees and high turnover, youre really starting in adeep hole, one that most managers cant dig their way out of. Costs

really do matter.George Gus Sauter, Manager of the Vanguard S&P500 Index Fund

Q 12


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Active or Passive Management?

Gr

oss(before

costs)

Net(aftercosts)

Gr

oss(before

costs)

Gr

oss(before

costs)

Net(aftercosts)

Net(aftercosts)


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Portfolios

A portfolio is a collection of different securities such as stocks and bonds,

that are combined and considered a single asset

The risk-return characteristics of the portfolio is demonstrably different

than the characteristics of the assets that make up that portfolio,

especially with regard to risk.

Combining different securities into portfolios is done to achieve

diversification.

Q 15


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Diversification

Diversification has two faces:

1. Diversification results in an overall reduction in portfolio risk (return

volatility over time) with little sacrifice in returns, and

2. Diversification helps to immunize the portfolio from potentiallycatastrophic events such as the outright failure of one of the

constituent investments.

(If only one investment is held, and the issuing firm goes bankrupt,

the entire portfolio value and returns are lost. If a portfolio is madeup of many different investments, the outright failure of one is more

than likely to be offset by gains on others, helping to make the

portfolio immune to such events.)

Q 15. a

Q 15


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Correlation

The degree to which the returns of two stocks co-move is

measured by the correlation coefficient ().

The correlation coefficient () between the returns on twosecurities will lie in the range of +1 through - 1.

+1 is perfect positive correlation

-1 is perfect negative correlation

BA

AB

AB

COV

[8-13]

Q 15 . c


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Covariance and Correlation Coefficient

Solving for covariance given the correlation

coefficient and standard deviation of the two

assets:

BAABABCOV [8-14]

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