Concept of Risk & Return.pptx help understand the risk and return

Risk and return PPT

1. RISK AND RETURN

2. OUTLINE Concept of risk and return Relationship between Risk and Return Risk and Return of a Single Asset Risk and Return of a Portfolio Measurement of Market Risk

3. Introduction It is important to understand the relation between risk and return due to uncertainty. The relation between risk and return is useful for investors (who buy/sell securities), corporations (that sell securities to finance themselves), and for financial intermediaries (that invest, borrow, lend, and price securities on behalf of their clients). The relationship between risk & return is fundamental in finance theory.

4. Introduction If given the choice between Investing in a low risk opportunity that says it will pay you a 10% return on your money. Investing in a high risk opportunity that says it will pay you a 10% return on your money. Most people would choose the lower risk opportunity. The principle we follow in finance is that investors need the inducement of higher reward to take on perceived higher risks

5. Defining a return on an Investment Investment returns measure the financial results of an investment. Returns may be historical or prospective/expected (anticipated). We invest in a stock to have positive return. For stocks, we have two components May receive Dividend Stock price may appreciate

6. Defining Historical Return Income received on an investment plus any change in market price , usually expressed as a percent of the beginning market price of the investment. D t + ( P t - P t-1 ) P t-1 R =

7. RISK AND RETURN OF A SINGLE ASSET Rate of Return Rate of Return = Annual income + Ending price-Beginning price Beginning price Beginning price Current yield Capital gains yield

8. Return Example The stock price for Stock A was Rs 10 per share 1 year ago. The stock is currently trading at Rs 11.50 per share and shareholders just received a Rs 1 dividend . What return was earned over the past year? 1.00 + ( 11.50 - 10.00 ) 10.00 R = = 2 5%

9. Return The previous example calculated what actually happened. We call this a “historic return”. (Its history) However, prior to making the investment, we may have had an expected return of 30%? In this case, What actually happened fell short of our expectation. Alternatively, may be our expectation was to earn only 10%. In this case the actual return exceeded our expectations.

10. Expected Return The future is uncertain. Investors do not know with certainty whether the economy will be growing rapidly or be in recession. Investors do not know what rate of return their investments will yield. Therefore, they base their decisions on their expectations concerning the future. The expected rate of return on a stock represents the mean of a probability distribution of possible future returns on the stock.

11. Expected Return The table below provides a probability distribution for the returns on stocks A and B State Probability Return On Return On Stock A Stock B 1 20% 5% 50% 2 30% 10% 30% 3 30% 15% 10% 4 20% 20% -10% The state represents the state of the economy one period in the future i.e. state 1 could represent a recession and state 2 a growth economy. The probability reflects how likely it is that the state will occur. The sum of the probabilities must equal 100%. The last two columns present the returns or outcomes for stocks A and B that will occur in each of the four states.

12. Expected Return Given a probability distribution of returns, the expected return can be calculated using the following equation: N E[R] = Σ (p i R i ) i=1 Where: E[R] = the expected return on the stock N = the number of states p i = the probability of state i R i = the return on the stock in state i.

13. Expected Return In this example, the expected return for stock A would be calculated as follows: E[R] A = .2(5%) + .3(10%) + .3(15%) + .2(20%) = 12.5% Now you try calculating the expected return for stock B!

14. Expected Return Did you get 20%? If so, you are correct. If not, here is how to get the correct answer: E[R] B = .2(50%) + .3(30%) + .3(10%) + .2(-10%) = 20% So we see that Stock B offers a higher expected return than Stock A. However, that is only part of the story; we haven't considered risk.

15. Risk The fact that what actually happens (and often does) differ from what we either expect or would like to happen is defined as risk. Its useful to have a mathematical tool to measure risk. A common approach is to look at expected returns and calculate the volatility of the returns. Volatility is measured either by SD or Variance. The larger the volatility, the greater the risk.

16. Defining Risk What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? Does it matter if it is a bank CD or a share of stock? The variability of returns from those that are expected.

17. What is Investment risk? Typically, investment returns are not known with certainty. The greater the chance of a return far below the expected return, the greater the risk. It is the potential for divergence between the actual outcome and what is expected. In finance, risk is usually related to whether expected cash flows will materialize, whether security prices will fluctuate unexpectedly, or whether returns will be as expected.

18. Probability distribution Rate of return (%) 50 15 -20 Stock X Stock Y Which stock is riskier? Why?

19. ‹#› Average Returns and St. Dev. for Asset Classes, 2000-2017 Investors who want higher returns have to take more risk The incremental reward from accepting more risk seems constant Bills Bonds Stocks Average Return (%) Standard Deviation (%)

20. Expected Risk & Preference Risk-averse investor Risk-neutral investor Risk-seeking investor

21. Measurement of Risk One way to measure risk is to calculate the variance and standard deviation of the distribution of returns. Standard Deviation, σ , is a statistical measure of the variability of a distribution around its mean. The larger the standard deviation, the higher the probability that returns will be far below the expected return. The variance is the sum of the squares of deviations of actual returns from the expected return, weighted by the associated probabilities.

22. Measurement of Risk - Formula

23. How to Determine the Expected Return and Standard Deviation Stock BW R i P i ( R i )( P i ) ( R i - R ) 2 ( P i ) -.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042 .00288 .33 .10 .033 .00576 Sum 1.00 .090 .01728

24. Determining Standard Deviation (Risk Measure) σ = Σ ( R i - R ) 2 ( P i ) σ = .01728 σ = .1315 or 13.15% n i=1

25. Measures of Risk Probability Distribution: State Probability Return On Return On Stock A Stock B 1 20% 5% 50% 2 30% 10% 30% 3 30% 15% 10% 4 20% 20% -10% E[R] A = 12.5% E[R] B = 20%

26. Measures of Risk The variance and standard deviation for stock A is calculated as follows: σ 2 A = .2(.05 -.125) 2 + .3(.1 -.125) 2 + .3(.15 -.125) 2 + .2(.2 -.125) 2 = .002625 σ Α = (.002625) 0.5 = .0512 = 5.12% Now you try the variance and standard deviation for stock B!

27. Measures of Risk σ 2 B = .2(.50 -.20) 2 + .3(.30 -.20) 2 + .3(.10 -.20) 2 + .2(-.10 - .20) 2 = .042 σ Β = (.042) 0.5 = .2049 = 20.49% Although Stock B offers a higher expected return than Stock A , it also is riskier since its variance and standard deviation are greater than Stock A 's.

28. Practice Question

29. Classification of risk Unique risk of a security represents that portion of its total risk which stems from company specific factors & not explained by general market movements. Also known as Unsystematic Risk . It is avoidable through diversification. Examples – Workers declare strike, Company loses a big contract, Emergence of a new competitor. Total Risk = Unique Risk +Market Risk

30. Continued…… Market risk of security represents that portion of its risk which is attributable to economy –wide factors. Also known as Systematic Risk . It is un avoidable. Examples - Changes in economy, tax reforms, Changes in interest rate policy, Inflation, Restrictive credit policy.

31. Market Risk (Systematic Risk) Total Risk Unsystematic risk Systematic risk STD DEV OF PORTFOLIO RETURN NUMBER OF SECURITIES IN THE PORTFOLIO

32. Unique Risk (Unsystematic risk) Total Risk Unsystematic risk Systematic risk STD DEV OF PORTFOLIO RETURN NUMBER OF SECURITIES IN THE PORTFOLIO

33. Portfolio Risk and Return Most investors do not hold stocks in isolation. Instead, they choose to hold a portfolio of several stocks. When this is the case, a portion of an individual stock's risk can be eliminated, i.e., diversified away. From our previous calculations, we know that: the expected return on Stock A is 12.5% the expected return on Stock B is 20% the variance on Stock A is .00263 the variance on Stock B is .04200 the standard deviation on Stock A is 5.12% the standard deviation on Stock B is 20.49%

34. Portfolio Risk and Return The Expected Return on a Portfolio is computed as the weighted average of the expected returns on the stocks which comprise the portfolio. The weights reflect the proportion of the portfolio invested in the stocks. This can be expressed as follows: N E[R p ] = Σ w i E[R i ] i=1 Where: E[R p ] = the expected return on the portfolio N = the number of stocks in the portfolio w i = the proportion of the portfolio invested in stock i E[R i ] = the expected return on stock i

35. Variance & Standard deviation of a Two-asset portfo l io For a portfolio consisting of two assets, the above equation can be expressed as: E[R p ] = w 1 E[R 1 ] + w 2 E[R 2 ] = w 1 E[R 1 ] +( 1-w 1 )E[R 2 ] If we have an equally weighted portfolio of stock A and stock B (50% in each stock), then the expected return of the portfolio is: E[R p ] = .50(.125) + .50(.20) = 16.25% The portfolio weight of a particular security is the percentage of the portfolio’s total value that is invested in that security.

36. Expected Return of a Portfolio Example Portfolio value = 2,000 + 5,000 = 7,000 r A = 14%, r B = 6%, w A = weight of security A = 2,000 / 7,000 = 28.6% w B = weight of security B = 5,000 / 7,000 = (1-28.6%)= 71.4%

37. PORTFOLIO RISK : THE 2-SECURITY CASE Risk of individual assets is measured by their variance or standard deviation. We can use variance or standard deviation to measure the risk of the portfolio of assets as well. The risk of portfolio would be less than the risk of individual securities, and that the risk of a security should be judged by its contribution to the portfolio risk.

38. PORTFOLIO RISK : THE 2-SECURITY CASE The variance/standard deviation of a portfolio reflects only the variance/standard deviation of the stocks that make up the portfolio and not how the returns on the stocks which comprise the portfolio vary together. Two measures of how the returns on a pair of stocks vary together are the covariance and the correlation coefficient. The portfolio variance or standard deviation depends on the co-movement of returns on two assets. Covariance of returns on two assets measures their co-movement. Correlation coefficient, is often used to measure the degree of co-movement between two variables. The correlation coefficient simply standardizes the covariance.

39. PORTFOLIO RISK : THE 2-SECURITY CASE The Covariance between the returns on two stocks can be calculated as follows: Cov(R A ,R B ) = σ A,B = Σ p i (R A - E[R A ])(R B - E[R B ]) Where: σ Α,Β = the covariance between the returns on stocks A and B p i = the probability of state R A = the return on stock A E[R A ] = the expected return on stock A R B = the return on stock B E[R B ] = the expected return on stock B

40. Covariance of Returns of Securities X and Y

41. PORTFOLIO RISK : THE 2-SECURITY CASE The Correlation Coefficient between the returns on two stocks can be calculated as follows: σ A,B Cov(R A ,R B ) Corr(R A ,R B ) = ρ A,B = σ A σ B = SD(R A )SD(R B ) Where: ρ A,B =the correlation coefficient between the returns on stocks A and B σ A,B =the covariance between the returns on stocks A and B, σ A =the standard deviation on stock A, and σ B =the standard deviation on stock B

42. Portfolio Risk and Return Using either the correlation coefficient or the covariance, the Variance on a Two-Asset Portfolio can be calculated as follows: σ 2 p = (w A ) 2 σ 2 A + (w B ) 2 σ 2 B + 2w A w B ρ A,B σ A σ B OR σ 2 p = (w A ) 2 σ 2 A + (w B ) 2 σ 2 B + 2w A w B σ A,B The Standard Deviation of the Portfolio equals the positive square root of the variance.

43. Portfolio Risk and Return: Example The covariance between stock A and stock B is as follows: σ A,B = .2(.05-.125)(.5-.2) + .3(.1-.125)(.3-.2) + .3(.15-.125)(.1-.2) +.2(.2-.125)(-.1-.2) = -.0105 The correlation coefficient between stock A and stock B is as follows: -.0105 ρ A,B = (.0512)(.2049) = -1.00

44. Portfolio Risk and Return Let’s calculate the variance and standard deviation of a portfolio comprised of 75% stock A and 25% stock B: σ 2 p =(.75) 2 (.0512) 2 +(.25) 2 (.2049) 2 +2(.75)(.25)(-1)(.0512)(.2049)= .00016 σ p = .00016 = .0128 = 1.28% Notice that the portfolio formed by investing 75% in Stock A and 25% in Stock B has a lower variance and standard deviation than either Stocks A or B and the portfolio has a higher expected return than Stock A. This is the purpose of diversification; by forming portfolios, some of the risk inherent in the individual stocks can be eliminated.

45. MEASUREMENT OF MARKET RISK THE SENSITIVITY OF A SECURITY TO MARKET MOVEMENTS IS CALLED BETA . BETA REFLECTS THE SLOPE OF A THE LINEAR REGRESSION RELATIONSHIP BETWEEN THE RETURN ON THE SECURITY AND THE RETURN ON THE PORTFOLIO Relationship between Security Return and Market Return   Security Return          Market return  

46. CAPITAL ASSET PRICING MODEL(CAPM) EXPECTED RATE OF RISK-FREE RATE OF + RISK RETURN RETURN PREMIUM RISK PREMIUM = BETA [EXPECTED RETURN ON MARKET PORTFOLIO – RISK FREE RATE OF RETURN] Example Beta = 1.20 Expected return on the market portfolio = 15 percent Risk free rate = 10 percent Expected rate of return = 10 +1.2 (15-10) = 16 percent = +

47. Rate of Return C Risk premium for an aggressive 17.5 B security 15.0 A 12.5 Risk premium for a neutral security R f = 10 Risk premium for a defensive security 0.5 1.0 1.5 2.0 Beta BETA (MARKET RISK) & EXPECTED RATE OF RETURN