Techniques for Portfolio Performance Measurement
Portfolio Performance
Measure – some techniques
by
Binam Ghimire
Objectives
Discussion on the topics of:
Portfolio Performance Evaluation
Raw Return Analysis
Risk Adjusted Return Techniques: Sharpe Ratio,
Treynor Ratio, Jensen Alpha, M
2
, Information Ratio,
Tracking Error, Modified Sharpe
Attribution Analysis
Measuring performance with multiple risk factors
2
3
Portfolio Managers
4
High Returns: Above Average
Low Risk: Eliminate unique risk (diversify)
Outperformance
Superior Timing
Superior Selection
French, K. R. (2008). Presidential address: The cost of active investing.
The
Journal of Finance
,
63
(4), 1537-1573.
Why is it difficult to beat the benchmark?
Boxplot diagram for peer group
comparison
Diamond for average return of fund
manager
Square for Benchmark average return
5
Portfolio Managers
Raw Returns
6
Arithmetic, Geometric, annualizing, HPR,
single period, multiple periods, other sub
periods ...
Statistically significant results
Composite Portfolio
Performance Measures
7
Treynor Portfolio Performance Measure
Sharpe Portfolio Performance Measure
Jensen Portfolio Performance Measure
Information Ratio Performance Measure
8
Treynor Ratio
Jack Treynor (1965)
The ratio of Portfolio excess
return to
Treynor, J. L. (1965). How to rate management of Investment Funds.
Harvard
Business Review
,
43
(1), 63-75.
William Sharpe (1966)
The ratio of Portfolio excess
return to
Sharpe, W. F. (1966) Mutual fund performance.
The Journal of
Business
,
39
(1),
119-138.
9
Sharpe Ratio
10
Jensen Measure
Michael C Jensen 1968
It is portfolio alpha, AKA Jensen alpha
=(total portfolio return – risk free rate)
– [portfolio beta x (market return – risk free rate)]
OR
= (R
p
– R
f
) – [
β
p
x (R
m
– R
f
)]
A measure of portfolio performance that uses the
portfolio Beta and CAPM to calculate its excess return
which can be positive, negative or zero
Jensen, M. C. (1968). The performance of mutual funds in the period 1945–
1964.
The Journal of finance
,
23
(2), 389-416
11
Information Ratio
Jack Treynor and Fisher Black in 1973
Ratio of alpha to the standard deviation of
diversifiable risk
Denominator is TE
Treynor, J. L., & Black, F. (1973). How to use security analysis to
improve portfolio selection.
The journal of business
,
46
(1), 66-86.
Modigliani, F., & Leah, M. (1997). Risk-adjusted
performance.
Journal of Portfolio Management
,
23
(2), 45-
54.
12
Modigliani and Modigliani
Leah Modigliani and Franco Modigliani, 1997
13
Performance Measurement with Downside Risk
Israelson (2005)
Israelsen, C. (2005). A refinement to the Sharpe ratio and
information ratio.
Journal of Asset Management
,
5(6),
423-
427.
14
Modified Sharpe Ratio
MSR = ER/SD
(ER/absER)
15
Performance Attribution Analysis
16
Measuring Performance with
Multiple Risk Factors
Applying the Jensen measure
Alphas can be calculated relative to three
– four – five … factors
Style-like analysis
Explore various techniques for evaluating portfolio performance, including raw return analysis, risk-adjusted return metrics like Sharpe Ratio and Treynor Ratio, and composite portfolio performance measures. Learn about measuring performance with multiple risk factors and the challenges faced by portfolio managers in beating benchmarks.
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Presentation Transcript
Portfolio Performance Measure some techniques by Binam Ghimire
Objectives Discussion on the topics of: Portfolio Performance Evaluation Raw Return Analysis Risk Adjusted Return Techniques: Sharpe Ratio, Treynor Ratio, Jensen Alpha, M2, Information Ratio, Tracking Error, Modified Sharpe Attribution Analysis Measuring performance with multiple risk factors 2
Portfolio Managers High Returns: Above Average Low Risk: Eliminate unique risk (diversify) [E(R), f E(U) = 2 ] Outperformance Superior Timing Superior Selection French, K. R. (2008). Presidential address: The cost of active investing. The Journal of Finance, 63(4), 1537-1573. Why is it difficult to beat the benchmark? 4
Portfolio Managers Boxplot diagram for peer group comparison Diamond for average return of fund manager Square for Benchmark average return 5
Raw Returns Arithmetic, Geometric, annualizing, HPR, single period, multiple periods, other sub periods ... Statistically significant results 6
Composite Portfolio Performance Measures Treynor Portfolio Performance Measure Sharpe Portfolio Performance Measure Jensen Portfolio Performance Measure Information Ratio Performance Measure 7
Treynor Ratio Jack Treynor (1965) ( ) r P E r = f T P The ratio of Portfolio excess return to Treynor, J. L. (1965). How to rate management of Investment Funds. Harvard Business Review, 43 (1), 63-75. 8
Sharpe Ratio William Sharpe (1966) The ratio of Portfolio excess return to ( ) P E r r = f S P P Sharpe, W. F. (1966) Mutual fund performance. The Journal of Business, 39(1), 119-138. 9
Jensen Measure Michael C Jensen 1968 It is portfolio alpha, AKA Jensen alpha =(total portfolio return risk free rate) [portfolio beta x (market return risk free rate)] OR = (Rp Rf) [ p x (Rm Rf)] A measure of portfolio performance that uses the portfolio Beta and CAPM to calculate its excess return which can be positive, negative or zero Jensen, M. C. (1968). The performance of mutual funds in the period 1945 1964. The Journal of finance, 23(2), 389-416 10
Information Ratio Jack Treynor and Fisher Black in 1973 Ratio of alpha to the standard deviation of diversifiable risk p = A Denominator is TE Treynor, J. L., & Black, F. (1973). How to use security analysis to improve portfolio selection. The journal of business, 46(1), 66-86. 11
Modigliani and Modigliani Leah Modigliani and Franco Modigliani, 1997 = 2 M (S S ) p M M Modigliani, F., & Leah, M. (1997). Risk-adjusted performance. Journal of Portfolio Management, 23 (2), 45- 54. 12
Performance Measurement with Downside Risk Sortino Measure, 1994 ?? ? ??? ???= 1 ? ??? ?? 2 ???= Sortino, F. A., & Price, L. N. (1994). Performance measurement in a downside risk framework. the Journal of Investing, 3(3), 59-64. 13
Modified Sharpe Ratio Israelson (2005) MSR = ER/SD(ER/absER) Israelsen, C. (2005). A refinement to the Sharpe ratio and information ratio. Journal of Asset Management, 5(6), 423- 427. 14
Performance Attribution Analysis Allocation Effect ??? ???? ??? ?? ? Selection Effect ???? ??? ??? ? 15
Measuring Performance with Multiple Risk Factors Applying the Jensen measure ? ??? ?? = ??+ ?1??1?+ ?2??2?+ + ?????? Alphas can be calculated relative to three four five factors ??? ?? = ? + ????????+ ????????+ ????????+ ??? Style-like analysis 16
