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  1. An Overview of Risk Adjusted Methods BY CA. Pramod Prabhu. S.H., B.Sc, A.C.A,C.I.S.A (U.S.A)

  2. Risk & Uncertainty • Risk: The variability of actual return from the expected returns associated with a given asset/investment is defined as Risk • The greater the variability, the riskier the security • Uncertainty: Involves a situation where the likelihood of Possible outcomes is not known, whereas Risk refers to a situation where the decision maker knows the consequence of a particular decision & their related likelihoods

  3. Types of Risk • Systematic Risk: • Refers to that portion of variation in returns caused by factors that affect the price of all securities. Here the price of all individual securities move in same direction, generally due to response to economic, social & political changes. • Cannot be eliminated by diversification of Portfolio, because all the component securities are affected • Factors causing the Risk: • 1. Market Risk: Variations in Prices sparked off due to social, political or economic events • 2. Interest Rate Risk: Generally price of securities are inversely proportional to change in interest rates. The monetary & credit policy being non-controllable by the investors affects the riskiness of investments due to their effects on return expectations and the total principal amount to be refunded

  4. Types of Risk • 3. Purchasing Power Risk: • Arising due to Inflation • II Unsystematic Risk: • Portion of Risk caused due to factors unique or related to a firm/Industry. This is company specific risk & can be controlled if proper measures are taken. It can be further divided into: • 1. Business Risk: Internal risk caused due to improper product mix, non availability of RM, absence of strategic management etc. External risks refer to risks thrust upon the firm like govt controls, change in laws, international market conditions etc. • 2. Financial Risk: Associated with Capital structure of the company. A company with no debt has no financial risk. • 3. Credit/default Risk: Deals with probability of meeting a default, i.e. the borrower becoming unable to payback

  5. Risk In Investment Evaluation • In Capital Budgeting decisions, we are making forecasts of CFs. But since future events are uncertain, forecasts cannot be made perfectly. • Thus, risk arises in investment decisions • Risk is associated with the variability of future events of a project. The greater the variability of expected returns, the riskier the project. Risk can however, be measured more precisely. Most common measures of risk are standard deviation & coefficient of variation • Statistical techniques are available for handling risky investments. These techniques drawn from fields of Mathematics, logic, economics & Psychology enable the decisionmaker make the decisions in conditions of uncertainty • Thus the concept of Probability is fundamental to the use of risk analysis techniques

  6. Risk In Investment Evaluation • Probability: Can be defined as the likelihood that an event will occur • If an event is certain to occur, we say that the probability of occurrence = 1 • If an event is certain not to occur, we say that the P(Occurrence) = 0 • Thus P (all events to occur) lies between 0 and 1 • Probability in CF forecast: • Future CF forecasts are a crucial part of CB decisions • A typical forecast is a single figure for a period, referred to as the best estimate or most likely forecast. • The problem with single figure forecast is that we do not know the chances of actual occurrence and also the meaning of ‘Best Estimate’ or ‘Most likely’ estimate is not clear • Hence the forecast should not give just one estimate but a range of associated probability, like High, low & best guess estimates

  7. Risk In Investment Evaluation • But still some info like the forecaster's degree of confidence in the forecasts is missing. This problem is overcome by assigning probabilities to the estimates, like, • Assigning Probabilities: • Objective Probability: Probability estimate which is made based on a large No. of observations. (Traditional Method) • Subjective Probability: Probability assignments that reflect the state of belief of a person rather than the objective evidence of a large No. of trials

  8. Risk In Investment Evaluation • Risk adjusted Methods – Expected Net Cash Flow: • Once the probability assignments are made to the future CFs, the E(Net Cash Flow) can be found as sum of (CFs x their probabilities) • Absolute Measure of Risk – Variance or Standard Deviation: • Through the calculation of Expected Net Cash flow and consequently, the expected NPV, risk is explicitly incorporated into CB analysis. But, a better picture will be obtained risk analysis, if, we find out the dispersion of cash flows, i.e. the difference between possible cash flows that can occur and their expected value. • The dispersion of cash flows indicates the degree of risk • A commonly used measure of Risk is the Standard deviation or Variance • Variance means the deviation about expected cash flow of each of the possible cash flows. SD is the square root of variance

  9. Risk In Investment Evaluation • Relative Measure of Risk – Coefficient of Variation: • In certain circumstances, it might be found that a project might have a larger SD & also a higher expected NPV. In such instances, the decision maker is in a dilemma as to the project to be chosen • To resolve such issues, instead of analysing risk in absolute terms it may be measured in relative terms • A relative measure of risk is the coefficient of variation • Coeff of V = (SD/Expected Value) • Benefits of coefficient of Variation: In comparison of Projects which have, • 1. Same SD but different Expected values • 2. Different SD but same expected values & • 3. Different SD and different expected values

  10. Conventional Risk Analysis Techniques • 1. Payback: • One of the oldest and commonly used methods for explicitly recognising risk associated with an investment Project • Business firms using this method usually prefer a short PB to longer ones and often establish guidelines that a firm should accept only those investments with PB not exceeding a certain No. of years • Merits: • Simplicity • Makes allowance for risk by focusing on near term future & thus emphasising the liquidity of firm through capital recovery & by preferring ST projects to longer ones

  11. Conventional Risk Analysis Techniques • Limitations: • 1. As a method of Risk analysis, it is useful only in allowing for a special type of Risk – the risk that a project will go on exactly as planned for a certain period and will then suddenly cease altogether and be worth nothing, i.e., it is more concerned with assessment of risks of time nature • This risk may arise due to conditions like civil war in a country, closure of business due to indefinite strike, introduction a new product by competitor which captures the whole market, natural disasters etc • But, usual risks are not these, but, the normal business risks that the CF forecasts might go wrong due to lower sales, higher costs etc • 2. Even as a method of allowing risks of a time nature, it ignores the Time Value of cash flows • Ex. Two projects with PB = 4 Years. In first, CFs occur evenly over the four years, while in second, entire CF is in 4th Year. Second one is riskier, as if the projects cease in 3rd year, entire capital is lost there

  12. Conventional Risk Analysis Techniques • 2. Risk adjusted Discount Rate: • According to the economic theorists, to allow for risk, the businessman required a premium over and above an alternative, which was risk-free. The more uncertain the future returns the greater the risk and greater the premium required. Accordingly, it is proposed that risk premium be incorporated into capital budgeting analysis through the discount rate • Thus, if, the time preference for money is to be recognised by discounting estimated future CFs to their PV at some risk free rate, then, to allow for riskiness of those CFs a risk premium rate may be added to the risk free discount rate. Such a composite discount rate called the risk adjusted discount rate will allow for both time preference & risk preference and will be a sum of risk free rate & risk premium rate reflecting the investor’s attitude towards risk • RADR = Risk free rate + Risk Premium

  13. Conventional Risk Analysis Techniques • 2. Risk adjusted Discount Rate: • Advantages: • 1. Simple & easy to understand • 2. Great deal of intuitive appeal for a risk averse businessman • 3. It incorporates an attitude (Risk aversion) towards uncertainty • Limitations: • 1. Calculating RADR not easy • 2. Based on assumption that investors are risk averse, which ignores those who do not demand premium for assuming risks

  14. Conventional Risk Analysis Techniques • 3. Certainty Equivalent: • Method used to reduce the forecasts of CFs to some conservative levels • Ex. If an investor, according to his best estimate, expects a CF of Rs. 60,000 next year, he will apply an intuitive correction factor and may work with Rs. 40,000 instead, to be on safer side. • The CE coefficient applied to the forecast CFs assumes a value between 0 & 1. These coefficients are decided subjectively/objectively by the decision maker • They represent the confidence of decision maker in obtaining a particular CF in a period • If a CF of Rs. 20,000 is expected in next year, but if he feels that only 80% is it a certain amount, then the CE coefficient is 0.80, i.e. he considers only Rs. 16,000 as certain CF • Thus, CE varies inversely with risk

  15. Conventional Risk Analysis Techniques • Certainty Equivalent - Limitations: • 1. Recognizes risk, but the procedure of reducing CF forecasts is implicit & likely to be inconsistent from one investment to another • 2. The forecaster expecting reduction that will be made in his forecasts may inflate them in anticipation. This will no longer give forecasts according to best estimate • 3. If the forecasts are to pass through several layers of management, the effect may be to exaggerate the original forecast or to make it ultra conservative

  16. Conventional Risk Analysis Techniques • RADR Vs CE: • The CE approach recognises risk in CB by adjusting the estimated CFs and employing risk free rate to discount the adjusted CFs. On the other hand, RADR adjusts for risk by adjusting the discount rate • It is suggested that the CE approach is theoretically a superior technique over the RADR, as it can measure risk more accurately • The assumption that risk is an increasing function of time may or may not be true in actual investment under consideration. In case of an investment which is more risky in its gestation period & less riskier as it becomes established, the use of a constant RADR is not suitable. But the increased/decreased risk can be suitably accounted for over a period of time by changing the CE coefficients. Hence, CE is considered superior • Also, selecting a the premium rate which measures the degree of increasing risk, to obtain the RADR is difficult. CE coefficients that specify different degree of risks are more practical to work out

  17. Sensitivity Analysis • Need: • In evaluation of an investment project, CF forecasts which are dependent on expected revenues & costs play a vital role. CFs depend on various variables like sales volume, costs etc. The NPV or IRR of a project is arrived at by analysing after-tax CFs arrived at by combining forecasts of various variables. It is difficult to arrive at an accurate & unbiased forecast of each variable. Hence the manager should be alert to the possibilities of variations in these variables. He should have an idea of the extent to which the key elements in the project can vary before the projects +ve NPV is turned to Zero. Sensitivity analysis is a technique used for the same • SA is the process where each estimated element of a project is taken in turn, keeping all other estimates constant, to study the extent to which it can vary, before the positive NPV is turned to zero. If the estimate element varies more than this, the decision advise given by NPV is incorrect

  18. Sensitivity Analysis • Aim: • Seek out those variables of a project that could have an adverse effect on overall outcome of an appraisal if they are to fall short of their expected values. It examines the degree to which the various estimates can change before the decision becomes wrong • Advantage: • 1. Highlights those estimates to which the decision advise is most sensitive • 2. Management can seek more information on those elements and consider actions to strengthen the weak areas • 3. Helps expose inappropriate forecasts and thus guides the decision-maker to concentrate on relevant variables • Limitations: • 1. Does not examine the effect of simultaneous change in two or more estimates • 2. Does not give any lead to the decision-maker with respect to risk measurement & further action to be taken

  19. Scenario Analysis • The simple sensitivity analysis assumes that variables are independent of each other. In practice the variables are inter-related & may change in combination • In such circumstances, the risk of an investment can be analysed by considering the impact of alternative combinations of variables, called scenarios, on the project’s NPV or IRR • For this the decision maker can develop certain plausible scenarios

  20. Decision Trees • In practice investment decisions are not simple accept-reject ones, but, may have implications for future investment decisions. Such complex investment decisions involve a sequence of decisions over time • Since present choices modify future alternatives, industrial activity cannot be reduced to a single decision & must be viewed as a sequence of decisions extending from present time into future. Hence investment expenditures need be viewed as links in a chain of present & future commitments. An analytical technique to handle sequential decisions is to employ decision trees • At time of taking decisions, the outcome of a chance event is not known but a probability distribution can be assigned to it • A decision tree is a graphic display of the relationship between a present decision and future events, future decisions & their consequences. The sequence of events are mapped out over time in a format similar to the branches of a tree

  21. Decision Trees • Steps: • 1. Decide on Investment required • 2. Identify Possibilities & assign Probabilities • 3. Draw the decision tree for Possible Outcomes for each year • 4. Compute the DCIF,DCOF & NPV for each outcome • 5. Compute Joint Probability for each outcome • 6. Compute Risk adjusted NPV for each outcome • 7. Compute the total risk adjusted NPV & see if the project can be selected

  22. Decision Trees • Uses: • Particularly useful to handle sequential investments. Working backwards from future to present, we are able to eliminate unprofitable branches and determine optimum decisions at various decision points • Clarity: Brings out implicit assumptions & calculations for all to see, question & revise • Graphic Visualisation: Enables decision maker to visualise assumptions & alternatives in graphic form, which is more understandable • Limitations: • With more alternatives & variables, it can become increasingly complicated

  23. Risk & Return of a Portfolio • A Portfolio is a bundle or combination of individual assets or securities • Return of a Portfolio = Weighted average return of individual securities of the Portfolio, the weightage being proportion of investment value in each asset • i.e. Total of [(Proportion of A x It’s return)+ (Proportion of B x It’s return)]*P for each situation • Risk of a Portfolio is not the wt ave of risk of individual securities. The Portfolio SD depends on co-movement of returns on the two assets. This is measured through co variance. • Co variance depends on correlation between the securities of the portfolio • A total reduction of risks is possible if the securities in the portfolio are perfectly negatively correlated. There is no advantage of diversification if the securities are perfectly positively correlated. A zero correlation coefficient means that there is no relationship between the returns of securities. Practically the correlation coefficient will vary between -1 & +1

  24. Risk & Return of a Portfolio • Correlation coefficient between the securities, A & B – [Cov AB/(SD A * SD B)] • Cov AB = sum of ( difference between return & expected return for each situation) x it’s P • Measuring Risk of a Portfolio – First Principle Method: • 1 Convert the Portfolio into a single security. • 2. Risk = √P * (X – E)² • X = Return of each security as given • E = Expected return of a security, computed. • Measuring Risk of a Portfolio – Formulae Method: • Risk AB = √[{(wA*¬A)+(wB*¬B)+2(wA*¬A)(wB*¬B)} * rAB] • wA & wB = Weights of securities A & B in the Portfolio • ¬A, ¬B = Risk of securities A & B • rAB = Correlation coefficient between A & B

  25. CAPM • Helps in valuation of an Asset • Is a model that provides a framework to determine the required rate of return on an asset & indicates the relationship between the return & risk of an asset • Here the Security Market Line exemplifies the relation between an asset’s risk & the required rate of return • Assumptions under CAPM: • 1. Market efficiency: Share prices reflect all available information. Individual investors are not able to affect security prices • 2. Risk-aversion: Investors are risk averse & want highest returns for a given level of risk • 3. Homogenous expectations: All investors have same expectations about the security risk & returns • 4. Single time period: All investor decisions are based on a single time period • 5. Risk free rate: All investors can borrow & lend at a risk free rate of interest

  26. CAPM- Explanation • Suppose risk free investment is 5%. Anybody who invests in risk free investments (Ex. T – bills, Govt Bonds) can earn this return. The stock market earns a certain rate of return, say 15%. If you invest in stocks that constitute the stock market index, you can earn 15%. The additional 10%, is the market risk premium, i.e. your reward for undertaking the additional risk. • If an investment is as risky as the stock market, you need a risk premium of 10%. If it is 30% riskier than stock market, it should carry a risk premium of (10% + 30% of 10%), i.e. 13%. How much more risky an investment is as compared to market is indicated by Beta. Hence risk premium a stock should earn is beta times the risk premium from market. The total return from the stock should be risk free rate of return + risk premium. This is indicated by CAPM.

  27. CAPM • E(r) = Rf + Þ [E(Rm) – Rf] • E(r) = Expected return of the security • Rf – Risk free rate of return • Þ – Security Beta (Rsm * ¬s/¬m) • E(Rm) – Expected return from market; [E(Rm) – Rf] – Market risk premium • Under CAPM, the risk of an individual risky security is defined as the volatility of the security’s return vis-à-vis return of the market portfolio • Limitations of CAPM: • 1. Assumptions are unrealistic • 2. Difficult to test it’s validity • 3. Betas do not remain stable over time • Note: A graphical representation of CAPM is SML (Security market Line)

  28. Beta • Þ – Security Beta (Rsm * ¬s/¬m) or [COVsm/Vm] • Beta represents the sensitivity of a security to the general market movements. Represents the degree of systematic risk for a security relative to the level of risk of all other securities in market • Beta of a stock measures it’s sensitivity with reference to a broad based market index. The index, in India, for example could be the sensex • A beta of 1.20 indicates that the stock is 20% riskier than the index • A beta of 0.90 indicates that the stock is 10% less risky than the market • Beta = 1 indicates that the stock is as risky as the market index • Use of Beta: • Beta > 1 = Stocks are riskier than market. They move faster than market . If market goes up, their value goes up faster & vice versa • Beta < 1 = Stocks are less riskier than market. They move slower than market . If market goes up, their value go up slower & vice versa • Beta = 1 = Stock mimics the market

  29. Beta • Limitations of Beta: • 1. Has limited predictive value in ascertaining the future movements in share prices vis-à-vis movements in market, as it is based on past data • 2. It measures only the volatility of expected return on a given security, relative to changes in market movements. It does not indicate the total volatility in expected return of a security • 3. Beta measures only one portion of volatility of return, i.e. which is caused by systematic risk. It does not measure all elements that cause the variability in returns in an asset

  30. Alpha • Beta is a measure of what should be the return on a single security/Portfolio relative to market return. • Alpha is an indicator of the extent to which the actual return of a stock deviates from those predicted by its beta value • Alpha of a well diversified Portfolio should be • Zero • A positive/negative alpha represents temporary abnormal returns • A share’s alpha value is a measure of its abnormal return and represents the amount (%) by which the share returns are currently above or below the required return, given its systematic risk • Steps in computation of Alpha: • 1. Compute return mandated by CAPM • 2. Compute the actual return for a set of observations • 3. Compute the difference between the two & find their simple average (= Alpha)

  31. Alpha • Interpretation: • Alpha values assume significance in Investment market. This helps an investor decide whether the stocks are under/over or rightly valued • Positive Alpha: • Indicates that E(R) could be higher than that mandated by CAPM, to the extent of Alpha value. These stocks are undervalued & hence are much sought after • Negative Alpha: • E (R) will be less than that mandated by CAPM to the extent of Alpha value. Stocks are over valued and to be sold • Sale of overvalued stocks & purchase of under valued stocks would mean that overtime, the value of stocks will touch the values suggested by CAPM & hence, alpha values will overtime become zero • Note: Alpha value has limited utility & no predictive value. Hence it cannot be taken as sole basis for a logical decision to invest or not in a share

  32. Arbitrage Pricing Theory • CAPM provides a link between E(R) on a share & the E (R) on Market Index. It assumes that investors will be rewarded only for non diversifiable risks. These risks can be traced to macro economic factors like interest rates, inflation, Gross national product, Forex Reserves etc. • These factors affect various businesses in varied manner, i.e. their impact is not alike. A company having overseas transactions might be severely affected by Forex fluctuations, while a company having local operations only, won’t be affected much. • Thus we can understand that the responsiveness of a business entity to each of these factors will be different. Hence, a business can have a Beta for a change in forex reserves, another Beta for a change in inflation rates & so on. • Using the sensitivity of the firm to two or more such factors that are relevant, the E (R) on a given stock can be estimated • E (R) = Rf + B1 (Rm-Inflation – Rf) + B2 (Rm-Forex – Rf) + B3 (Rm-GNP – Rf) etc. • Here B1, B2, B3 represent the company’s Beta for Inflation, Forex & GNP respectively

  33. THANK YOU