Portfolio Management Summary

1 SFM STRATEGIC FINANCIAL MANAGEMENT By CA. Gaurav Jain PORTFOLIO MANAGEMENT SUMMARY 100% Conceptual Coverage With Live Trading Session Complete Coverage of Study Material, Practice Manual & Previous year Exam Questions Registration Office: 1/50, Lalita park, Laxmi Nagar – Delhi 92 Contact Details: 08860017983, 09654899608 Mail Id: gjainca@gmail.com Web Site: www.sfmclasses.com FB Page: https://www.facebook.com/CaGauravJainSfmClasses CA. Gaurav Jain Strategic Financial Management 2 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS CA. Gaurav Jain Strategic Financial Management 3 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS CA. Gaurav Jain Strategic Financial Management 4 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS CA. Gaurav Jain Strategic Financial Management 5 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Some Average Students who scored Extra Ordinary Marks in SFM NAME MARKS ROLL NO. ANKUR AHUJA 81 118704 PRAVEEN KR. BANSAL 79 124614 SHUBHAM BANSAL 77 126553 VIPUL KOHLI 76 119771 SAMYAK JAIN 75 117279 SANYA BHUTANI 71 121320 MOHAN 70 120201 NAMAN JAIN 70 123182 ALOK JAIN 70 175378 PREETI GUPTA 70 120727 NISHANT BHARDWAJ 68 115218 SUMIT CHOPRA 65 121871 AMIT CHAWLA 65 145682 TARUN MEHROTRA 64 121080 RATAN BHADURIA 63 126331 ANAND KHANKANI 63 128791 CA. Gaurav Jain Strategic Financial Management 6 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Mark sheet of our Student – Pravesh Kumar Final Examination Result ROLL Number 125761 Name PRAVESH KUMAR Group I Financial Reporting 040 Strategic Financial Management 085 Advanced Auditing and Professional Ethics 048 Corporate and Allied Laws 056 Total 229 Result PASS Grand Total 229 Mark sheet of our Student - Ankur Ahuja Final Examination Result ROLL Number 118704 Name ANKUR AHUJA Group I Financial Reporting 046 Strategic Financial Management 081 Advanced Auditing and Professional Ethics 040 Corporate and Allied Laws 066 Total 233 Result PASS Grand Total 233 CA. Gaurav Jain Strategic Financial Management 7 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Mark sheet of our Student – Vipul Kohli Final Examination Result ROLL Number 119771 Name VIPUL KOHLI Group I Financial Reporting 052 Strategic Financial Management 076 Advanced Auditing and Professional Ethics 046 Corporate and Allied Laws 043 Total 217 Result PASS Group II Advanced Management Accounting 051 Information Systems Control and Audit 041 Direct Tax Laws 045 Indirect Tax Laws 046 Total 183 Result PASS Grand Total 400< CA. Gaurav Jain Strategic Financial Management 8 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Portfolio Management Attempt wise Marks Analysis of Chapter Attempts Marks May-2011 10 Nov-2011 0 May-2012 16 Nov-2012 8 May-2013 0 Nov-2013 8 May-2014 0 Nov-2014 8 May-2015 16 Nov-2015 0 10 0 16 8 0 8 0 8 16 00 2 4 6 8 10 12 14 16 18 May-2011Nov-2011May-2012Nov-2012May-2013Nov-2013May-2014Nov-2014May-2015Nov-2015 CA. Gaurav Jain Strategic Financial Management 9 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Concept No. 1: Introduction  Portfolio means combination of various underlying assets like bonds, shares, commodities, etc.  Portfolio Management refers to the process of selection of a bundle of securities with an objective of maximization of return & minimization of risk. Steps in Portfolio Management Process  Planning  Execution  Feedback Concept No. 2: Major return Measures (i) Holding Period Return (HPR) :- HPR is simply the percentage increase in the value of an investment over a given time period. HPR = &#-667558897;&#-667558869;&#-667558878;&#-667558884;&#-667558882; &#-667558886;&#-667558867; &#-667558867;&#-667558879;&#-667558882; &#-667558882;&#-667558873;&#-667558883;−&#-667558871;&#-667558869;&#-667558878;&#-667558884;&#-667558882; &#-667558886;&#-667558867; &#-667558867;&#-667558879;&#-667558882; &#-667558885;&#-667558882;&#-667558880;&#-667558880;&#-667558878;&#-667558873;&#-667558878;&#-667558873;&#-667558880;+&#-667558909;&#-667558878;&#-667558865;&#-667558878;&#-667558883;&#-667558882;&#-667558873;&#-667558883; &#-667558871;&#-667558869;&#-667558878;&#-667558884;&#-667558882; &#-667558886;&#-667558867; &#-667558867;&#-667558879;&#-667558882; &#-667558885;&#-667558882;&#-667558880;&#-667558880;&#-667558878;&#-667558873;&#-667558878;&#-667558873;&#-667558880; (ii) Arithmetic Mean Return :- It is the simple average of a series of periodic returns. = &#-667558895;&#-667557937;+ &#-667558895;&#-667557936;+&#-667558895;&#-667557935;+&#-667558895;&#-667557934;+⋯+&#-667558895;&#-667558873; &#-667558873; Concept No. 3: Calculation of Return of an individual security 1. Average Return :- Step 1: Calculate HPR for different years, if it is not directly given in the Question. Step 2: Calculate Average Return i.e. ∑&#-667558889; &#-667558873; 2. Expected Return (Expected Value):- E(x) = ∑&#-667558897;&#-667558889;&#-667558878;&#-667558889;&#-667558878; = &#-667558897;&#-667558889;&#-667557937;&#-667558889;&#-667557937;+&#-667558897;&#-667558889;&#-667557936;&#-667558889;&#-667557936;+&#-667558897;&#-667558889;&#-667557935;&#-667558889;&#-667557935;+⋯+&#-667558897;&#-667558889;&#-667558873;&#-667558889;&#-667558873; Return Average Return Based on Past Data Expected Return Based on Probability CA. Gaurav Jain Strategic Financial Management 10 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Concept No. 4: Calculation of Risk of an individual security Risk of an individual security will cover under following heads: 1. Standard Deviation of Security (S.D) :- (S.D) or σ (sigma) is a measure of total risk / investment risk. Based on Past Data:- Formula (σ) = √∑(&#-667558889;−&#-667558889;̅ )&#-667557936; &#-667558873; Note: For sample data, we may use (n-1) instead of n in some cases. x = Given Data x̅ = Average Return n = No. of events/year Note: ∑(X− X̅ ) will always be Zero Based on Probability:- S.D (σ ) = √∑&#-667558871;&#-667558869;&#-667558872;&#-667558885;&#-667558886;&#-667558885;&#-667558878;&#-667558875;&#-667558878;&#-667558867;&#-667558862;(&#-667558889;−&#-667558889;̅ )&#-667557936; Where x̅ = Expected Return Note:  ∑(X− X̅ ) may or may not be Zero in this case.  S.D can never be negative. It can be zero or greater than zero.  S.D of risk-free securities or government securities or U.S treasury securities is always assumed to be zero unless, otherwise specified in question. Decision: Higher the S.D, Higher the risk and vice versa. Standard Deviation Based on Past DataBased on Probability CA. Gaurav Jain Strategic Financial Management 11 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS 2. Variance Based on Past Data:- Variance = (S.D) 2 = (σ) 2 Variance = ∑(&#-667558889;−&#-667558889;̅ )&#-667557936; &#-667558873; Based on Probability:- Variance = ∑&#-667558871;&#-667558869;&#-667558872;&#-667558885;&#-667558886;&#-667558885;&#-667558878;&#-667558875;&#-667558878;&#-667558867;&#-667558862;(&#-667558889;−&#-667558889;̅ )&#-667557936; Decision: Higher the Variance, Higher the risk and vice versa. 3. Co-efficient of Variation (CV) :- CV is used to measure the risk (variable) per unit of expected return (mean) Formula: CV = &#-667558894;&#-667558867;&#-667558886;&#-667558873;&#-667558883;&#-667558886;&#-667558869;&#-667558883; &#-667558909;&#-667558882;&#-667558865;&#-667558878;&#-667558886;&#-667558867;&#-667558878;&#-667558872;&#-667558873; &#-667558872;&#-667558881; &#-667558889; &#-667558912;&#-667558865;&#-667558882;&#-667558869;&#-667558886;&#-667558880;&#-667558882;/&#-667558908;&#-667558863;&#-667558871;&#-667558882;&#-667558884;&#-667558867;&#-667558882;&#-667558883; &#-667558865;&#-667558886;&#-667558875;&#-667558866;&#-667558882; &#-667558872;&#-667558881; &#-667558889; Decision: Higher the C.V, Higher the risk and vice versa. Concept No. 5: Rules of Dominance in case of an individual Security or when two securities are given Rule No. 1: X Ltd. Y Ltd σ 5 5 Return 10 15 Decision:- Select Y. Ltd.  For a given 2 securities, given same S.D or Risk, select that security which gives higher return. Rule No. 2: X Ltd. Y Ltd σ 5 10 Return 15 15 Decision:- Select X. Ltd.  For a given 2 securities, given same return, select which is having lower risk in comparison to other. CA. Gaurav Jain Strategic Financial Management 12 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Rule No. 3: X Ltd. Y Ltd σ 5 10 Return 10 25 Decision:- Based on CV (Co-efficient of Variation).  When Risk and return are different, decision is based on CV. CV x = 5/10 = 0.50 CV y = 10/25 = 0.40 Decision:- Select Y. Ltd. Concept No. 6: Calculation of Return of a Portfolio of assets  It is the weighted average return of the individual assets/securities. Where, W i = Market Value of investments in asset Market Value of the Portfolio  Sum of the weights must always =1 i.e. W A + W B = 1 Concept No. 7: Risk of a Portfolio of Assets Standard Deviation of a Two-Asset Portfolio σ1,2 = √ ��&#-667557937;&#-667557936;&#-667558864;&#-667557937;&#-667557936;+ ��&#-667557936;&#-667557936;&#-667558864;&#-667557936;&#-667557936;+&#-667557936;��&#-667557937;&#-667558864;&#-667557937;��&#-667557936;&#-667558864;&#-667557936;&#-667558869;&#-667557937;,&#-667557936; where r1,2 = Co-efficient of Co-relation; σ 1 = S.D of Security 1; σ 2 = S.D of Security 2; w1 = Weight of Security 1; w2 = Weight of Security 2 Portfolio Return Based on Past Data RP or RA+B= Avg. ReturnAxWA+ Avg. ReturnBxWB Based on Probability RP or RA+B= Expected ReturnAxWA + Expected ReturnBxWB CA. Gaurav Jain Strategic Financial Management 13 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS 1) Co-efficient of Correlation r 1,2 = &#-667558910;&#-667558872;&#-667558865;&#-667557937;,&#-667557936; ��&#-667557937;��&#-667557936; Or Cov1,2 = r1,2 σ1 σ2  The correlation co-efficient has no units. It is a pure measure of co-movement of the two stock’s return and is bounded by -1 and +1. 2) Co-Variance Cov X,Y = ∑( &#-667558889;− &#-667558889;̅ ) ( &#-667558888;− &#-667558888;̅) &#-667558873; Cov X,Y = ∑ &#-667558897;&#-667558869;&#-667558872;&#-667558885;.(&#-667558889;− &#-667558889;̅)(&#-667558888;− &#-667558888;̅) Note: Co-Variance or Co-efficient of Co-relation between risk-free security & risky security will always be zero. Concept No. 8: Portfolio risk as Correlation varies Note:  The portfolio risk falls as the correlation between the asset’s return decreases.  The lower the correlation of assets return, the greater the risk reduction (diversification) benefit of combining assets in a portfolio.  If assets return when perfectly negatively correlated, portfolio risk could be minimum. Portfolio Diversification refers to the strategy of reducing risk by combining many different types of assets into a portfolio. Portfolio risk falls as more assets are added to the portfolio because not all assets prices move in the same direction at the same time. Therefore, portfolio diversification is affected by the: Co-Variance Based on Past DataBased on Probability CA. Gaurav Jain Strategic Financial Management 14 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS 1. Correlation between assets: Lower correlation means greater diversification benefits. 2. Number of assets included in the portfolio: More assets means greater diversification benefits. Concept No. 9: Standard-deviation of a 3-asset Portfolio ��&#-667557937;,&#-667557936;,&#-667557935; = √��&#-667557937;&#-667557936;&#-667558890;&#-667557937;&#-667557936;+ ��&#-667557936;&#-667557936;&#-667558890;&#-667557936;&#-667557936;+ ��&#-667557935;&#-667557936;&#-667558890;&#-667557935;&#-667557936;+ &#-667557936; ��&#-667557937;��&#-667557936;&#-667558890;&#-667557937;&#-667558890;&#-667557936; &#-667558869;&#-667557937;,&#-667557936;+&#-667557936; ��&#-667557937;��&#-667557935; &#-667558890;&#-667557937;&#-667558890;&#-667557935;&#-667558869;&#-667557937;,&#-667557935; +&#-667557936; ��&#-667557936;��&#-667557935;&#-667558890;&#-667557936;&#-667558890;&#-667557935; &#-667558869;&#-667557936;,&#-667557935; Or ��&#-667557937;,&#-667557936;,&#-667557935; = √��&#-667557937;&#-667557936;&#-667558890;&#-667557937;&#-667557936;+ ��&#-667557936;&#-667557936;&#-667558890;&#-667557936;&#-667557936;+ ��&#-667557935;&#-667557936;&#-667558890;&#-667557935;&#-667557936;+ &#-667557936; &#-667558890;&#-667557937;&#-667558890;&#-667557936;&#-667558910;&#-667558872;&#-667558865;&#-667557937;,&#-667557936;+&#-667557936; &#-667558890;&#-667557937;&#-667558890;&#-667557935;&#-667558910;&#-667558872;&#-667558865;&#-667557937;,&#-667557935; +&#-667557936; &#-667558890;&#-667557936;&#-667558890;&#-667557935;&#-667558910;&#-667558872;&#-667558865;&#-667557936;,&#-667557935; Portfolio consisting of 4 securities ��&#-667557937;,&#-667557936;,&#-667557935;,&#-667557934; = √ ��&#-667557937;&#-667557936;&#-667558890;&#-667557937;&#-667557936;+ ��&#-667557936;&#-667557936;&#-667558890;&#-667557936;&#-667557936;+ ��&#-667557935;&#-667557936;&#-667558890;&#-667557935;&#-667557936;+��&#-667557934;&#-667557936;&#-667558890;&#-667557934;&#-667557936;+&#-667557936; ��&#-667557937;��&#-667557936;&#-667558890;&#-667557937;&#-667558890;&#-667557936; &#-667558869;&#-667557937;,&#-667557936; +&#-667557936; ��&#-667557936;��&#-667557935;&#-667558890;&#-667557936;&#-667558890;&#-667557935; &#-667558869;&#-667557936;,&#-667557935;+ &#-667557936; ��&#-667557935;��&#-667557934; &#-667558890;&#-667557935;&#-667558890;&#-667557934;&#-667558869;&#-667557935;,&#-667557934; +&#-667557936; ��&#-667557934;��&#-667557937; &#-667558890;&#-667557934;&#-667558890;&#-667557937;&#-667558869;&#-667557934;,&#-667557937; +&#-667557936; ��&#-667557936;��&#-667557934; &#-667558890;&#-667557936;&#-667558890;&#-667557934;&#-667558869;&#-667557936;,&#-667557934; +&#-667557936; ��&#-667557937;��&#-667557935; &#-667558890;&#-667557937;&#-667558890;&#-667557935;&#-667558869;&#-667557937;,&#-667557935; Concept No. 10: Standard Deviation of Portfolio consisting of Risk-free security & Risky Security We know that S.D of Risk-free security is ZERO. σ A,B = √ ��&#-667558912;&#-667557936;&#-667558864;&#-667558912;&#-667557936;+ ��&#-667558911;&#-667557936;&#-667558864;&#-667558911;&#-667557936;+&#-667557936;��&#-667558912;&#-667558864;&#-667558912;��&#-667558911;&#-667558864;&#-667558911;&#-667558869;&#-667558912;,&#-667558911; = √ ��&#-667558912;&#-667557936;&#-667558864;&#-667558912;&#-667557936;+&#-667557938;+&#-667557938; = σA WA Concept No. 11: Calculation of Portfolio risk and return using Risk-free securities and Market Securities  Under this we will construct a portfolio using risk-free securities and market securities. Case 1: Investment 100% in risk-free (RF) & 0% in Market Risk = 0% [S.D of risk free security is always 0(Zero).] Return = risk-free return Case 2: Investment 0% in risk-free (RF) & 100% in Market Risk = σ m Return = R m CA. Gaurav Jain Strategic Financial Management 15 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Case 3: Invest part of the money in Market & part of the money in Risk-free Return = R m W m + RF W Rf Risk of the portfolio = σ m × Wm (σ of RF = 0) Case 4: Invest more than 100% in market portfolio. Addition amount should be borrowed at risk-free rate. Let the additional amount borrowed weight = x Return of Portfolio = R m× (1+ x) – RF × x Risk of Portfolio = σ m × (1+ x) Concept No. 12: Optimum Weights For Risk minimization, we will calculate optimum weights. Formula : WA = �� &#-667558911;&#-667557936; − &#-667558910;&#-667558872;&#-667558865;&#-667558886;&#-667558869;&#-667558878;&#-667558886;&#-667558873;&#-667558884;&#-667558882; (&#-667558912;,&#-667558911;) �� &#-667558912;&#-667557936; + �� &#-667558911;&#-667557936; – &#-667557936;× &#-667558910;&#-667558872;&#-667558865;&#-667558886;&#-667558869;&#-667558878;&#-667558886;&#-667558873;&#-667558884;&#-667558882; (&#-667558912;,&#-667558911;) WB = 1- WA (Since WA + WB = 1) We know that Covariance (A,B) = r A,B × σ A × σ B Note:  When r = -1 i.e. two stocks are perfectly (-) correlated, minimum risk portfolio become risk-free portfolio. WA = ��&#-667558807; ��&#-667558808; + ��&#-667558807; Concept No. 13: CAPM (Capital Asset Pricing Model) For Individual Security: The relationship between Beta (Systematic Risk) and expected return is known as CAPM. Required return/ Expected Return = Risk-free Return + &#-667558911;&#-667558882;&#-667558867;&#-667558886; &#-667558868;&#-667558882;&#-667558884;&#-667558866;&#-667558869;&#-667558878;&#-667558867;&#-667558862; &#-667558911;&#-667558882;&#-667558867;&#-667558886; &#-667558900;&#-667558886;&#-667558869;&#-667558876;&#-667558882;&#-667558867; (Return Market – Risk free return) OR = RF + β s (R m – RF) Note:  Market Beta is always assumed to be 1.  Market Beta is a benchmark against which we can compare beta for different securities and portfolio.  Standard Deviation & Beta of risk free security is assumed to be Zero (0) unless otherwise stated. CA. Gaurav Jain Strategic Financial Management 16 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS  R m – R F = Market Risk Premium.  If Return Market (R m) is missing in equation, it can be calculated through HPR (Holding Period Return)  R m is always calculated on the total basis taking all the securities available in the market.  Security Risk Premium = β (R m – R F) For Portfolio of Securities: Required return/ Expected Return = RF + βPortfolio (R m – RF) Concept No. 14: Decision Based on CAPM Case Decision Strategy Estimated Return/ HPR < CAPM Return Over-Valued Sell Estimated Return/ HPR > CAPM Return Under-Valued Buy Estimated Return/ HPR = CAPM Return Correctly Valued Buy, Sell or Ignore  CAPM return need to be calculated by formula, RF + β (R m – RF)  Actual return / Estimated return can be calculated through HPR Concept No. 15: Systematic Risk, Unsystematic risk & Total Risk Total Risk (��) = Systematic Risk (β) + Unsystematic Risk Unsystematic Risk (Controllable Risk):-  The risk that is eliminated by diversification is called Unsystematic Risk (also called unique, firm-specific risk or diversified risk). They can be controlled by the management of entity. E.g. Strikes, Change in management, etc. Systematic Risk (Uncontrollable Risk):-  The risk that remains can’t be diversified away is called systematic risk (also called market risk or non-diversifiable risk). This risk affects all companies operating in the market. CA. Gaurav Jain Strategic Financial Management 17 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS  They are beyond the control of management. E.g. Interest rate, Inflation, Taxation, Credit Policy Concept No. 16: Interpret Beta/ Beta co-efficient / Market sensitivity Index  The sensitivity of an asset’s return to the return on the market index in the context of market return is referred to as its Beta. Calculation of Beta 1. Beta Calculation with % change Formulae Beta = &#-667558910;&#-667558879;&#-667558886;&#-667558873;&#-667558880;&#-667558882; &#-667558878;&#-667558873; &#-667558894;&#-667558882;&#-667558884;&#-667558866;&#-667558869;&#-667558878;&#-667558867;&#-667558862; &#-667558895;&#-667558882;&#-667558867;&#-667558866;&#-667558869;&#-667558873; &#-667558910;&#-667558879;&#-667558886;&#-667558873;&#-667558880;&#-667558882; &#-667558878;&#-667558873; &#-667558900;&#-667558886;&#-667558869;&#-667558876;&#-667558882;&#-667558867; &#-667558895;&#-667558882;&#-667558867;&#-667558866;&#-667558869;&#-667558873; Note:  This equation is normally applicable when two return data is given.  In case more than two returns figure are given, we apply other formulas. 2. Beta of a security with co-variance Formulae Beta = &#-667558910;&#-667558872;−&#-667558891;&#-667558886;&#-667558869;&#-667558878;&#-667558886;&#-667558873;&#-667558884;&#-667558882; &#-667558872;&#-667558881; &#-667558912;&#-667558868;&#-667558868;&#-667558882;&#-667558867;′&#-667558868; &#-667558869;&#-667558882;&#-667558867;&#-667558866;&#-667558869;&#-667558873; &#-667558864;&#-667558878;&#-667558867;&#-667558879; &#-667558900;&#-667558886;&#-667558869;&#-667558876;&#-667558882;&#-667558867; &#-667558895;&#-667558882;&#-667558867;&#-667558866;&#-667558869;&#-667558873; &#-667558891;&#-667558886;&#-667558869;&#-667558878;&#-667558886;&#-667558873;&#-667558884;&#-667558882; &#-667558872;&#-667558881; &#-667558900;&#-667558886;&#-667558869;&#-667558876;&#-667558882;&#-667558867; &#-667558895;&#-667558882;&#-667558867;&#-667558866;&#-667558869;&#-667558873; = COVi.m ����2 3. Beta of a security with Correlation Formulae We know that Correlation Co-efficient (rim) = COVi.m σiσm to get Cov im = rim σiσm Substitute Cov im in β equation, We get β i = rimσiσm σm2 β = rim ��&#-667558878; ��&#-667558874; Concept No. 17: Beta of a portfolio It is the weighted average beta of individual security. Formula: Beta of Portfolio = Beta X Ltd. × W X Ltd. + Beta Y Ltd. × W Y Ltd. Where, W i = Market Value of investments in asset Market Value of the Portfolio CA. Gaurav Jain Strategic Financial Management 18 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Concept No. 18: Arbitrage Pricing Theory/ Stephen Ross’s Apt Model Overall Return = Risk free Return + {Beta Inflation × Inflation differential or factor risk Premium} + {Beta GNP × GNP differential or Factor Risk Premium} ……. & So on. Where, Differential or Factor risk Premium = [Actual Values – Expected Values] Concept No. 19: Evaluation of the performance of a portfolio (Also used in Mutual Fund) 1. Sharpe’s Ratio (Reward to Variability Ratio):  It is excess return over risk-free return per unit of total portfolio risk.  Higher Sharpe Ratio indicates better risk-adjusted portfolio performance. Formula: &#-667558895;&#-667558897;− &#-667558895;&#-667558907; ��&#-667558897; Where RP = Return Portfolio σ P = S.D of Portfolio Note:  Sharpe Ratio is useful when Standard Deviation is an appropriate measure of Risk.  The value of the Sharpe Ratio is only useful for comparison with the Sharpe Ratio of another Portfolio. 2. Treynor’s Ratio (Reward to Volatility Ratio):  Excess return over risk-free return per unit of Systematic Risk (β ) Formula: &#-667558895;&#-667558897;− &#-667558895;&#-667558907; ��&#-667558897; Decision: Higher the ratio, Better the performance. 3. Jenson’s Measure/Alpha:  This is the difference between a fund’s actual return & CAPM return Formula: α P = RP – (RF + β (R m – RF)) Or Alpha = Actual Return – CAPM Return It is excess return over CAPM return. CA. Gaurav Jain Strategic Financial Management 19 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS  If Alpha is +ve, performance is better.  If Alpha is -ve , performance is not better. 4. Market Risk - return trade – off:  Excess return of market over risk-free return per unit of total market risk. Formula: &#-667558895;&#-667558900;− &#-667558895;&#-667558907; ��&#-667558900; Decision: Higher is better. Concept No. 20: When two risk-free returns are given We are taking the Average of two Rates. Concept No. 21: Effect of Increase & Decrease in Inflation Rates Increase in Inflation Rates: Revised RF = RF + Increased Rate Revised RM = RM + Increased Rate Decrease in Inflation Rates: Revised RF = RF - Decreased Rate Revised RM = RM - Decreased Rate Concept No. 22: Characteristic Line (CL) Characteristic Line represents the relationship between Asset excess return and Market Excess return. Equation of Characteristic Line: Y = α + β x CA. Gaurav Jain Strategic Financial Management 20 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Where Y = Average return of Security x = Average Return of Market α = Intercept i.e. expected return of an security when the return from the market portfolio is ZERO, which can be calculated as Y – β × X = α b = Beta of Security Note: The slope of a Characteristic Line is COVi,M σM2 i.e. Beta Concept No. 23: New Formula for Co-Variance using Beta New Formula for Co-Variance between 2 Stocks (Cov A,B) = β A × β B × σ 2 m Concept No. 24: Co-variance of an Asset with itself is its Variance Cov (m,m) = Variance m Co-variance Matrix In Co-variance matrix, we present the co-variance among various securities with each other. Return Covariance A B C A xxx xxx xxx B xxx xxx xxx C xxx xxx xxx Concept No. 25: Sharpe Index Model or Calculation of Systematic Risk (SR) & Unsystematic Risk (USR)  Risk is expressed in terms of variance. Total Risk (TR) = Systematic Risk (SR) + Unsystematic Risk (USR) For an Individual Security: σ e i 2 = USR/ Standard Error/ Random Error/ Error Term/ Residual Variance. Total Risk = σs2 Systematic Risk (%) SR = βs2x σm2 Unsystematic Risk (%) σei 2 USR = TR -SR = σs2-βs2x σm2 CA. Gaurav Jain Strategic Financial Management 21 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS For A Portfolio of Securities: Concept No. 26: Co-efficient of Determination  Co-efficient of Determination = (Co-efficient of co-relation) 2 = r 2  Co-efficient of determination (r2) gives the percentage of variation in the security’s return i.e. explained by the variation of the market index return. Example: If r2 = 18%  In the X Company’s stock return, 18% of the variation is explained by the variation of the index and 82% is not explained by the index.  According to Sharpe, the variance explained by the index is the systematic risk. The unexplained variance or the residual variance is the Unsystematic Risk. Use of Co-efficient of Determination in Calculating Systematic Risk & Unsystematic Risk: 1. Explained by Index [Systematic Risk] = Variance of Security Return × Co-efficient of Determination of Security i.e. σ12 × r2 2. Not Explained by Index [Unsystematic Risk] = Variance of Security Return × (1 - Co-efficient of Determination of Security ) i.e. σ12 × (1 - r2) Concept No. 27: Portfolio Rebalancing  Portfolio re-balancing means balancing the value of portfolio according to the market condition. Total Risk = σP2 or = ( ∑ W iβ i )2x σ2m + ∑ W i2x USR i Systematic Risk (%) SR = βP2x σm2 ( ∑ W iβ i )2x σ2m Unsystematic Risk (%) USR = TR -SR = σP2-βP2x σm2 ∑ W i2x USR i CA. Gaurav Jain Strategic Financial Management 22 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS  Three policy of portfolio rebalancing: (a) Buy & Hold Policy : [“Do Nothing” Policy] (b) Constant Mix Policy: [“Do Something” Policy] (c) Constant Proportion Portfolio Insurance Policy (CPPI): [“Do Something” Policy] Value of Equity (Stock) = m × [Portfolio Value – Floor Value], Where m = multiplier  The performance feature of the three policies may be summed up as follows: (a) Buy and Hold Policy (ii) Gives rise to a straight line pay off. (iii) Provides a definite downside protection. (iv) Performance between Constant mix policy and CPPI policy. (a) Constant Mix Policy (i) Gives rise to concave pay off drive. (ii) Doesn’t provide much downward protection and tends to do relatively poor in the up market. (ii) Tends to do very well in flat but fluctuating market. (a) CPPI Policy (i) Gives rise to a convex pay off drive. (ii) Provides good downside protection and performance well in up market. (iii) Tends to do very poorly in flat but in fluctuating market. Note:  If Stock market moves only in one direction, then the best policy is CPPI policy and worst policy is Constant Mix Policy and between lies buy & hold policy.  If Stock market is fluctuating, constant mix policy sums to be superior to other policies. CA. Gaurav Jain Strategic Financial Management 23 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Concept No. 28: Modern Portfolio Theory/ Markowitz Portfolio Theory/ Rule of Dominance in case of selection of more than two securities Under this theory, we will select the best portfolio with the help of efficient frontier. Efficient Frontier:  Those portfolios that have the greatest expected return for each level of risk make up the efficient frontier.  All portfolios which lie on efficient frontier are efficient portfolios. Efficient Portfolios: Rule 1: Those Portfolios having same risk but given higher return. Rule 2: Those Portfolios having same return but having lower risk. Rule 3: Those Portfolios having lower risk and also given higher returns. Rule 4: Those Portfolios undertaking higher risk and also given higher return In-efficient Portfolios: Which don’t lie on efficient frontier. Solution Criteria: For selection of best portfolio out of the efficient portfolios, we must consider the risk-return preference of an individual investor.  If investors want to take risk, invest in the Upper End of efficient frontier portfolios.  If investors don’t want to take risk, invest in the Lower End of efficient frontier portfolios. Concept No. 29: Capital Market Line (CML) The line of possible portfolio risk and Return combinations given the risk-free rate and the risk and return of a portfolio of risky assets is referred to as the Capital Allocation Line. CA. Gaurav Jain Strategic Financial Management 24 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS  Under the assumption of homogenous expectations (Maximum Return & Minimum Risk), the optimal CAL for investors is termed the Capital Market Line (CML).  CML reflect the relationship between the expected return & total risk (σ). Equation of this line:- E(R p) = RF + ��&#-667558871; ��&#-667558874; [E (RM) – RF] Where [E (RM) – RF] is Market Risk Premium Concept No. 30: SML (Security Market Line)  SML reflects the relationship between expected return and systematic risk (β) Equation: E (R i) = RFR + &#-667558910;&#-667558898;&#-667558891;&#-667558878;,&#-667558900;&#-667558886;&#-667558869;&#-667558876;&#-667558882;&#-667558867; ��&#-667558874;&#-667558886;&#-667558869;&#-667558876;&#-667558882;&#-667558867;&#-667557936; [E (R Market) – RFR] Beta  If Beta = 0 CAPM Return = R f + β (R m – R f) = R f  If Beta = 1 E(R) = R f + β (R m – R f) = R f + R m – R f = R m Graphical representation of CAPM is SML.  According to CAPM, all securities and portfolios, diversified or not, will plot on the SML in equilibrium. CA. Gaurav Jain Strategic Financial Management 25 100% Coverage with Practice Manual and last 10 attempts Exam Papers solved in CLASS Concept No. 31: Cut-Off Point or Sharpe’s Optimal Portfolio Calculate Cut-Off point for determining the optimum portfolio Steps Involved Step 1: Calculate Excess Return over Risk Free per unit of Beta i.e. Ri− Rf βi Step 2: Rank them from highest to lowest. Step 3: Calculate Optimal Cut-off Rate for each security. Cut-off Point of each Security C i = σm2∑(&#-667558895;&#-667558878;− &#-667558895;&#-667558881;× ��) ��&#-667558882;&#-667558878;&#-667557936;&#-667558899;&#-667558878;=&#-667557937; 1+ σm2∑��&#-667558878;&#-667557936; ��&#-667558882;&#-667558878;&#-667557936;&#-667558899;&#-667558878;=&#-667557937; Step 4: The Highest Cut-Off Rate is known as “Cut-off Point”. Select the securities which lies on or above cut-off point. Step 5: Calculate weights of selected securities in optimum portfolio. (a) Calculate Z i of Selected Security Z I = βi σei2 [(Ri− Rf) βi− Cut off Point] (b) Calculate weight percentage Wi = ��i ∑��