Fund performance Measurement

1. “Investment Analysis & Portfolio Management”
Presenter Name:
Sami Ullah 17131554-002
M Abdul-Hanan 17821554-008
Muhammad Umar 18221554-007

2. Risk
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• Risk is defined in financial terms as the chance that an
outcome or investment's actual gains will differ from
an expected outcome or return.
• Risk includes the possibility of losing some or all of
an original investment.
• Risk takes on many forms but is broadly categorized
as the chance an outcome or investment's actual gain
will differ from the expected outcome or return.
• Risk includes the possibility of losing some or all of
an investment.
• There are several types of risk and several ways to
quantify risk for analytical assessments.
• Risk can be reduced using diversification and hedging
strategies.

3. Sources Of Risk
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1. Interest Rate Risk
2. Market Risk
3. Inflation Risk
4. Business Risk
5. Financial Risk
6. Liquidity Risk
7. Currency Risk (Exchange Rate Risk)
8. Country Risk

4. Measuring Risk
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• The level of volatility, or the variation between
actual and expected returns, is used to calculate
risk. The standard deviation is the measurement
of this difference.
Variance A statistical term measuring
dispersion—the standard deviation squared.
Standard Deviation measure of the dispersion
in outcomes around the expected value

5. Return
Return:
“Return is the motivating force in the investment
process.
It is the reward for undertaking the investment”.
Two Components Of Asset Return:
• Yield
The income component of a security’s return
• Capital Gain (Loss)
The change in price on security over some period

6. Return
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TOTAL RETURN
• Percentage measure relating all cash flows on a
security for a given time period to its purchase price
RETURN RELATIVE
• The total return for an investment for a given period
stated on the basis of 1.0

7. R E T U R N
Cumulative Wealth Index
 Cumulative wealth over time, given an initial wealth and a series of
returns on some asset
Currency Risk
 The risk of an adverse impact on the return from a foreign
investment as a result of movements in currencies.

8. A Framework for Evaluating and
Assessing Portfolio Performance
 We will consider four broad issues in evaluating portfolio performance:
1. Performance Measurement Issues—The critical concern for most
investors is to correctly determine how a portfolio performed over some
period of time. Thus, the portfolio’s results have to be correctly
measured and analyzed.
2. Well Known Measures of Performance—Several risk-adjusted
measures of portfolio performance have been available for many years.
One or more of these are often referred to in discussions of portfolio
performance, and therefore investors need to be aware of them.
3. Performance Attribution and Style Analysis—Going beyond
measuring a portfolio’s performance, the concept of performance
attribution seeks to determine why a portfolio had the rate of return it
did over some specified period of time. This relates to style analysis,
which describes a portfolio manager’s investing style.
4. Portfolio Presentation Standards—How should the actual results of a
portfolio be presented to those directly affected by that portfolio—in
other words, from investment manager to client? Fifteen years ago there
were few standards or guidelines. Now there are a clearly stated set of
standards to be followed when presenting portfolio results.

9. • A mutual fund is a company that pools money from
many investors and invests the money in securities such
as stocks, bonds, and short-term debt. The combined
holdings of the mutual fund are known as its portfolio.
Investors buy shares in mutual funds.
• The performance of Mutual funds can be measured/
evaluated through the following ways.
I. Alpha
II. Beta
III. R-Squared
IV. Standard Deviation
V. Sharp Ratio
VI. Trynor Ratio
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Mutual Fund & Ways To
Measure Performance

10. Alpha α
• Alpha refers to excess returns earned on an investment
above the benchmark return.
• Active portfolio managers seek to generate alpha in
diversified portfolios, with diversification intended to
eliminate unsystematic risk.
• Because alpha represents the performance of a portfolio
relative to a benchmark, it is often considered to represent
the value that a portfolio manager adds to or subtracts from
a fund's return.
• An alpha of 1.0 means the fund has outperformed its
benchmark index by 1%. Correspondingly, an alpha of -1.0
would indicate an underperformance of 1%. For investors,
the higher the alpha the better.
• Calculation of Alfa.
Alfa = Rp – [ Rf + (Rm –Rf) B* ]
Portfolio Return 16
Market Return 14
Risk Free Return 6.25
Beta 0.8 1 1.3
Alfa 3.55 2 -0.325

11. Beta β
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• Beta, primarily used in the capital asset pricing
model (CAPM), is a measure of the volatility–or
systematic risk–of a security or portfolio compared
to the market as a whole.
• Beta data about an individual stock can only provide
an investor with an approximation of how much risk
the stock will add to a (presumably) diversified
portfolio.
• 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. 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 is
theoretically 20% more volatile than the market.

12. Standard Deviation σ
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• Standard deviation measures the dispersion of data from its mean. In finance, standard
deviation is applied to the annual rate of return of an investment to measure its volatility
(risk). A volatile stock would have a high standard deviation. With mutual funds, the standard
deviation tells us how much the return on a fund is deviating from the expected returns based
on its historical performance.
• It is used to check the deviation of all returns from expected returns based on historical data,
therefore standard deviation is a popular way to measure the volatility of a fund.
• The higher the deviation is the higher is the funds volatility and risk and vice versa.

13. Sharp Ratio
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• Developed by Nobel laureate economist
William Sharpe.
• The Sharpe ratio measures risk-adjusted
performance.
• It shows us how much performance
additional return we are earning for every
unit of risk we undertake by buying a unit of
the mutual fund.
• Its is the ratio of the risk –adjusted return to
the volatility of the fund which is shown by
Standard deviation
• It is calculated by subtracting the risk-free
rate of return from the rate of return for an
investment and dividing the result by the
investment's standard deviation of its
return.
• Formula for Calculating Sharp Ratio
 S.R = Excess Return / S.D
 Excess Return = Rp - Rf
• Sharp ratio greater than >1.0 is Considered acceptable
“Good” by investors.
• Sharp ratio greater than >2.0 is rated as “Very Good”
• Sharp ratio is 3.0 = or Higher is Considered as “
Excellent”
• Ration under < 1.0 is “Sub optimal”
• The higher  the Sharp Ratio, the better performing an
investment is, and Vice Versa

14. R-Squared R2
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• R-Squared is a measure to find a fund’s
Correlation to its benchmark performance.
• This is done on the scale of 100 which means if
the R2 = 100 then it shows that the performance
the mutual fund is perfectly correlated with the
performance of benchmark.
• According to Morningstar, a mutual fund with an
R-squared value between 85 and 100 has a
performance record that is closely correlated to
the index.
• A fund rated 70 or less typically does not perform
like the index.
R2 = 100
Benchmark
Fund

15. Sortino Ratio
 The Sortino ratio is a variation of the Sharpe ratio that
differentiates harmful volatility from total overall volatility
by using the asset's standard deviation of negative portfolio
returns—downside deviation—instead of the total standard
deviation of portfolio returns.
 The Sortino ratio takes an asset or portfolio's return and
subtracts the risk-free rate, and then divides that amount by
the asset's downside deviation.
 The ratio was named after Frank A. Sortino.
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Formula and Calculation of Sortino Ratio
Sortino Ratio = Rp - Rf
r
where:
Rp​=Actual or expected portfolio return
Rf=Risk-free rate
σd​=Standard deviation of the downside​

16. Table 1. Performance Measure of Mutual Funds in
Pakistan for the period 2018 to 2021
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Name of the fund
Annual Return
Ri Rf
Ri- Rf
2018 2019 2020 2021
Abbott Lab (Pakistan) Ltd. -0.287 -0.019 -0.049 -0.051 -0.102 0.118 -0.220
Alfalah Consumer Index ETF -0.263 -0.133 -0.103 -0.162 -0.165 0.118 -0.283
Al-Ghazi Tractors Ltd 0.026 -0.021 0.109 -0.083 0.008 0.118 -0.110
Air Link Communication. -0.158 0.002 -0.202 -0.131 -0.122 0.118 -0.240
Atlas Battery Ltd. -0.217 -0.056 -0.085 -0.179 -0.134 0.118 -0.252
Altern Energy Ltd. -0.06 -0.078 -0.212 -0.021 -0.093 0.118 -0.211
Aisha Steel Ltd. 0.017 -0.041 0.254 -0.434 -0.051 0.118 -0.169
Aisha Steel Ltd. Balance 0.102 -0.004 -0.101 -0.022 -0.006 0.118 -0.124
Atlas Honda Ltd. 0.174 -0.018 -0.234 0.050 -0.007 0.118 -0.125

17. Performance Measure of Mutual Funds in Serbia for
the period 2018 to 2021
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Calculate the performance of Funds in Pakistan
• Formula for Calculating Sharp Ratio
 S.R = Excess Return / S.D
 Excess Return = Ri - Rf
1. S.R = -0.220/ 0.125 = -1.763
2. S.R = -0.283/ 0.069 = -4.077*
3. S.R = -0.110/ 0.081 = -1.362
4. S.R = -0.240/ 0.088 = -2.735
5. S.R = -0.252/ 0.076 = -3.312
6. S.R = -0.211/ 0.083 = -2.540
7. S.R = -0.169/ 0.285 = -0.592*
8. S.R = -0.124/ 0.084 = -1.487
9. S.R = -0.125/ 0.171 = -0.730
Name of the
fund
Annual Return
Ri Ri-Rf
St
Dev
Sharpe
ratio
2018 2019 2020 2021
Abbott Lab
(Pakistan) Ltd. -0.287 -0.019 -0.049 -0.051 -0.102 -0.220 0.125 -1.763
Alfalah
Consumer
Index ETF
-0.263 -0.133 -0.103 -0.162 -0.165 -0.283 0.069 -4.077
Al-Ghazi
Tractors
Ltd
0.026 -0.021 0.109 -0.083 0.008 -0.110 0.081 -1.362
Air Link
Communicat
ion.
-0.158 0.002 -0.202 -0.131 -0.122 -0.240 0.088 -2.735
Atlas
Battery Ltd. -0.217 -0.056 -0.085 -0.179 -0.134 -0.252 0.076 -3.312
Altern Energy
Ltd. -0.06 -0.078 -0.212 -0.021 -0.093 -0.211 0.083 -2.540
Aisha Steel Ltd. 0.017 -0.041 0.254 -0.434 -0.051 -0.169 0.285 -0.592
Aisha Steel
Ltd. Balance 0.102 -0.004 -0.101 -0.022 -0.006 -0.124 0.084 -1.487
Atlas Honda
Ltd. 0.174 -0.018 -0.234 0.050 -0.007 -0.125 0.171 -0.730
Note: The average annual rate of return on
treasury bills of the NBS for the period 2018-2021
was 11.8% (Rf = 0.118).
Source: Authors’ calculation

18. Table 2. Performance Of Mutual Funds In Pakistan
For The Period 2018-2021
Name of funds 2018 2019 2020 2021 Ri Rf RM Ri- Rf RM-RF b SD SR TR ALPHA
Abbott Lab (Pakistan) Ltd. -0.287 -0.019 -0.049 -0.051 -0.102 0.118 -0.063 -0.22 -0.18 -0.50 0.125 -1.76 0.444 0.310
Alfalah Consumer Index ETF -0.263 -0.133 -0.103 -0.162 -0.165 0.118 0.072 -0.28 -0.05 -0.37 0.069 -4.10 0.775 0.300
Al-Ghazi Tractors Ltd 0.026 -0.021 0.109 -0.083 0.008 0.118 0.041 -0.11 -0.08 -0.28 0.081 -1.36 0.394 0.131
Air Link Communication. -0.158 0.002 -0.202 -0.131 -0.122 0.118 -0.052 -0.24 -0.17 0.11 0.088 -2.73 -2.162 0.221
Atlas Battery Ltd. -0.217 -0.056 -0.085 -0.179 -0.134 0.118 0.066 -0.25 -0.05 -0.34 0.076 -3.32 0.748 0.270
Altern Energy Ltd. -0.060 -0.078 -0.212 -0.021 -0.093 0.118 0.083 -0.21 -0.03 0.42 0.083 -2.54 -0.502 0.196
Aisha Steel Ltd. 0.017 -0.041 0.254 -0.434 -0.051 0.118 -0.032 -0.17 -0.15 -0.90 0.285 -0.59 0.188 0.304
Aisha Steel Ltd. Balance 0.102 -0.004 -0.101 -0.022 -0.006 0.118 0.063 -0.12 -0.05 0.46 0.084 -1.48 -0.271 0.099
Atlas Honda Ltd. 0.174 -0.018 -0.234 0.050 -0.007 0.118 0.035 -0.13 -0.08 1.00 0.171 -0.73 -0.125 0.042

19. Thank
you
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