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Risk and Return Variability or uncertainty Of returns Gains received by Way of income + increase in Market value Presented By: Monu Jain CH Institute Of Management & Communication
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REALIZED RETURN & EXPECTED RETURN Historic or realized return as in case of a bank deposit at a fixed rate of interest. EXPECTED RETURN Have to be sufficiently high to offset the risk or uncertainty. Invest in Equity or not
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MEANING OF CASH Periodic cash receipts by way of interest, Dividends. Eg. Yield on a 10% bond of Rs. 900 is 11.11% The appreciation/depreciation in the price of the asset. i.e. difference between purchase & sale price of assets. Components Of Return
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Objectives : How to calculate Return ? What are its components How do we Measure risk What is Portfolio ? What is Capital asset Pricing model ? What is risks ? What are its Components ?
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Therefore RETURNS are measured as - <ul><li>Shares of company A were purchased for Rs.3580 and were sold for Rs.3800 after one year and dividend of Rs.35 was paid for the year how much is rate of return ? </li></ul>Regular cash flow Capital appreciation In value of security Initial capital Invested.
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How to measure return? Dividend regular cash flow Change in the value of stock over t -time Value of stock in beginning
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PROBABILITIES & RULES <ul><li>A probability can never be larger than 1 </li></ul><ul><li>The sum total of probability must be equal to 1 </li></ul><ul><li>A probability can never be negative </li></ul><ul><li>Certain to occur P=1 never occur P=0 </li></ul><ul><li>Probability should be mutually & collectively exhaustive. </li></ul>
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Let us take the case of HLL from 1991-1998 71.29 21.04 20.23 15.90 92.33 36.12 ? ? 33 249.60 1998 ? ? 25.50 207.60 1997 49.52 20.03 29.49 18.75 121.20 1996 22.71 16.95 5.76 15.00 93.60 1995 16.52 13.91 2.61 12.00 88.50 1994 70.54 15.14 55.41 8.4 86.25 1993 149.70 25.46 124.24 6.3 55.50 1992 - 24.75 1991 Rate of return (%) Dividend Yield (%) Capital gain Pt -P t-1 / P t-1 Dividend per share Share price (Pt) Year
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Expected returns <ul><li>The anticipated income over some future period and may be subject to certain risk or uncertainty is expected return. </li></ul><ul><li>Suppose in case of Alpha Ltd, following information – </li></ul><ul><li>1. 20% chance of 50% return </li></ul><ul><li>2. 30% chance of 40% return </li></ul><ul><li>3. 25% chance of 30% return </li></ul><ul><li>4. 25% chance of 10% return </li></ul><ul><li>=(0.20 x 0.50)+(0.30 x 0.40) +(0.25 x 0.30)+ (0.25 x 0.10) </li></ul><ul><li>= 32% </li></ul>
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Risk components Uncertainty of return is Market risk Liquidity risk Interest rate risk inverse Inflation risk Business risk Financial risk
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Calculation of risk <ul><li>Probability Distribution </li></ul><ul><li>Range </li></ul><ul><li>Variance </li></ul><ul><li>Standard deviation </li></ul>
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<ul><li>Say if following data is given to you ,of Alpha ltd., </li></ul>Probability distribution method – graphical method PROBABILITY RETURN Since the dispersion is near the y axis and not spread over the risk in this company is very low. -30% 0.1 -10% 0.2 10% 0.4 30% 0.2 50% 0.1 Rate of return Probability
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<ul><li>Say if following data is given to you ,of Beta ltd. </li></ul>Probability distribution method – graphical method PROBABILITY RETURN Since the dispersion is far from the y axis and spread over the risk in this company is very high -50% 0.1 -30% 0.2 10% 0.4 50% 0.2 70% 0.1 Rate of return Probability
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Range <ul><li>It is the difference between the highest and the lowest value of rate of return </li></ul><ul><li>It is based on only two extreme values. </li></ul><ul><li>Range for Ala ltd = 50% –( -30%) </li></ul><ul><li>= 80% </li></ul><ul><li>Range for Beta ltd= 70% - (-50%) </li></ul><ul><li>=120% </li></ul><ul><li>. So beta is more risky </li></ul>
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Variance <ul><li>It is the sum of the squared deviation of each possible rate of return from the expected rate of return multiplied by the probability that the rate of return occurs. </li></ul>
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Standard Deviation <ul><li>It is the square root of variance of the rate of return explained initially. </li></ul>
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Sources Of Risk <ul><li>Interest Rate Risk -Security prices move inversely to interest rates. </li></ul><ul><li>Market Risk- Variability of returns due to fluctuations in security markets. (Equity most affected) </li></ul><ul><li>Inflation Risk -Reduction in purchasing power. </li></ul><ul><li>Directly related to interest rate risk. </li></ul>
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Sources Of Risk <ul><li>Business Risk -Carrying on a business in a particular environment. The risk is transferred to the investors. </li></ul><ul><li>Financial Risk- greater the debt financing, greater the risk. </li></ul><ul><li>Liquidity Risk- Security which can be bought or sold easily, without significant price concession, is considered liquid. The greater the uncertainty about the time element & price concession, the greater the liquidity risk. </li></ul><ul><li>Treasury bills have ready markets lesser liquidity risks </li></ul>
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How to reduce risk ? <ul><li>If I invest in a company trading in sunglasses my normal observation would be that I experience good profits in summer and loss in rains </li></ul><ul><li>If I invest in a company trading in raincoats I would experience good profits during rainy season and losses during summers. </li></ul>
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Portfolio <ul><li>Keep all types of assets like – equity, </li></ul><ul><ul><ul><ul><ul><li>- bond, saving account </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>- real estate </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>- bullions </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>- collectibles and other </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>assets. </li></ul></ul></ul></ul></ul>Group of asset so that the total risk reduces
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I have to invest in two companies <ul><li>There are two companies – Company A and Company B . </li></ul><ul><li>The return from Company A is 12% and Company B is 18% </li></ul><ul><li>The standard deviation of A is 16% and 24% </li></ul><ul><li>Then how much will I invest in A and how much in B ie. The weights assigned to each will decide my total risk and return factor </li></ul>
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What will be the return and risk if I invest 50:50 in company A and company B <ul><li>A . 15 % return and 20 % risk </li></ul><ul><li>15 % return and 4 % risk </li></ul><ul><li>C. 15 % return and 14.42 % risk </li></ul><ul><li>The answer will depend on the relationship between Company A and Company B </li></ul>
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Formula to calculate risk in portfolio is – standard deviation of the portfolio Standard deviation of The security Relationship of The two securities
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Total Risk can be reduced through diversification <ul><li>Perfectly positively co-related – ex. Two leading companies in pharmaceutical industry. </li></ul><ul><li>Portfolio risk will be calculated as the addition of the risk of the securities in the portfolio. </li></ul><ul><li>Say, in given case </li></ul><ul><li>=(0.5*16) 2 + (0.5*24) 2 + 2 *0.5*16*0.5*24* 1 </li></ul><ul><li>= 0.5*16 + 0.5*24 </li></ul><ul><li>= 20% </li></ul><ul><li>No advantage of diversification </li></ul>
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Risk can be reduced through diversification <ul><li>Perfectly negatively co-related – ex. Two companies in raincoat and sunglass industry. </li></ul><ul><li>Portfolio risk will be calculated as the difference of the risk of the securities in the portfolio. </li></ul><ul><li>Say, in given case </li></ul><ul><li>=(0.5*16) 2 + (0.5*24) 2 - 2 *0.5*16*0.5*24* 1 </li></ul><ul><li>= 0.5*16 - 0.5*24 </li></ul><ul><li>= 4% </li></ul><ul><li>Huge advantage of diversification </li></ul>
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Risk can be reduced through diversification <ul><li>Perfectly not co-related – ex. Two companies in steel and fertilizer industry. </li></ul><ul><li>Portfolio risk will be calculated by following method. </li></ul><ul><li>Say, in given case </li></ul><ul><li>=(0.5*16) 2 + (0.5*24) 2 + 2 *0.5*16*0.5*24* 0 </li></ul><ul><li>=(0.5*16) 2 + (0.5*24) 2 </li></ul><ul><li>= 14.42% </li></ul><ul><li>Advantage of diversification to some extent </li></ul>
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RISK <ul><li>DIVERSIFIABLE/ unique risk </li></ul><ul><li>NON – DIVERSIFIABLE or systematic risk </li></ul>Changes in government policies – monetary policy, fiscal policy, foreign policy, corporate taxes War Earthquake, floods, rains, tsunamis etc. Strikes Increase in competition Technical breakdown or obsolescence Inadequate raw material Change in management. Loss of a big contract etc.
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Hence though initially the risk gets diversified, due to some systematic or market risk the diversification cannot completely negate the risk
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Number of securities in portfolio Risk Risk Reduction through diversification. Non – diversifiable Risk Diversifiable Risk The effect reduces with No change in market risk Increase in the portfolio size
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Similarly if we calculate Return of Alpha– 12% and Beta – 18% and std. deviation – Alpha -16% and Beta – 24%
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If we plot the data on a graph Efficient frontier Inefficient frontier Cor = - 1.0 Cor = - 0.25 Cor = + 1.0 Cor = + 0.50 Cor = - 1.0 alfa beta
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We will now try to analyze more of diversifiable (market risk) and non- diversifiable risk <ul><li>For this we will try to find relation between market risk and specific risk of the security </li></ul><ul><li>We try to analyse the responsiveness of security to general market and measure how extensively the return of security vary with changes in market return. </li></ul>
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Calculation of risk of a stock/ portfolio with respect to market <ul><li>We try to fit a line to find the systematic relationship (linear) between the return of security and the return of market. </li></ul><ul><li>As per model of William Sharpe it is expressed as – </li></ul>Return on Security J Relation between the market security and the security k Return above market at all times
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Calculation of beta <ul><li>Beta refers to the regression co-efficient between the market security and the portfolio returns. </li></ul>
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Capital Asset Pricing Model <ul><li>The capital asset pricing model (CAPM) is a model that provides a framework to determine the required rate of return on an asset and indicates the relationship between return and risk of the asset. </li></ul><ul><li>Assumptions of CAPM </li></ul><ul><ul><li>Market efficiency </li></ul></ul><ul><ul><li>Risk aversion and mean-variance optimisation </li></ul></ul><ul><ul><li>Homogeneous expectations </li></ul></ul><ul><ul><li>Single time period </li></ul></ul><ul><ul><li>Risk-free rate </li></ul></ul>
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Security Market Line <ul><li>For a given amount of systematic risk ( ), SML shows the required rate of return </li></ul> = (covar j,m / 2 m ) SLM E(R j ) R m R f 1.0 0
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Defensive securities EXPECTED / REQUIRED RATE OF RETURN ON Y AXIS RISK PREMIUM FOR UNCERTAINTY Aggressive securities Beta 1.0 Km Rf SML
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Defensive securities EXPECTED / REQUIRED RATE OF RETURN ON Y AXIS RISK PREMIUM FOR UNCERTAINTY Aggressive securities Beta 1.0 Km Rf SML X Y
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Types of investors – based on risk <ul><li>A risk-averse investor will choose among investments with the equal rates of return, the investment with lowest standard deviation. Similarly, if investments have equal risk (standard deviations), the investor would prefer the one with higher return. </li></ul><ul><li>A risk-neutral investor does not consider risk, and would always prefer investments with higher returns. </li></ul><ul><li>A risk-seeking investor likes investments with higher risk irrespective of the rates of return. In reality, most (if not all) investors are risk-averse. </li></ul>
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