Topic 4
Risk and Return
Learning Objectives
 Define risk and return.
 Identify risk and return relationship.
 Calculate expected return and sta...
Return represents the total gain or loss on an investment.
You invested in 1 share of Apple (AAPL) for $95 and sold
a year...
Expected return is what you expect to earn from an
investment in the future.
It is estimated as the average of the possibl...
• Risk is defined as the chance of suffering a financial
loss. Or the potential variability in future cash flows.
• Risk m...
Relationship between risk and return
• Standard deviation (S.D.) is one way to measure risk. It
measures the volatility or riskiness of returns. (σ -sigma)
• S...
State of Probability Return
Economy (P)
Company A Company B
Recession 0.20 4% -10%
Normal 0.50 10% 14%
Boom 0.30 14% 30%
k...
Company A
( 4% - 10%)2
(.2) = 7.2
(10% - 10%)2
(.5) = 0
(14% - 10%)2
(.3) = 4.8
Variance = 12
Stand. dev. = 12 = 3.46%
Com...
The coefficient of variation, CV, is a measure of relative
dispersion that is useful in comparing risks of assets with
dif...
Return Measurement for a Single Asset:
Expected Return (cont.)
Risk Measurement for a Single
Asset: Standard Deviation (cont.)
Table 1 The
Calculation of
the Standard
Deviation
of the R...
• An investment portfolio is any collection or combination of
financial assets.
• If we assume all investors are rational ...
‡ Portfolio: Hold /Invest in different types of assets (or
investments) at the same time or period.
 Combining several s...
 Diversification: spreading out of investments to reduce risks.
‡ Investments across different securities rather than in...
‡ If two stocks are perfectly positively correlated, diversification has
NO effect on risk. i.e If correlation (r) = +1, ...
 Investors should NOT expect to eliminate all risk from their
portfolio. Some risk can be diversified away and some canno...
Investment risks
 Market portfolio is a portfolio consisting of a weighted sum
of every asset in the market, with weights in the proportio...
 Systematic risk called non-diversifiable risk because it is beyond
the control of the investor and the firm.
ƒ Systemat...
Market returns and assets returns for certain period can be determined by
looking at the percentage of changes in index or...
 The slope of the line (beta), represents the average movement of
the firm’s stock returns in response to a movement in t...
 Beta is a measure of how an individual stock’s returns
vary with market returns.
 Beta measures of the sensitivity of a...
Portfolio beta indicates the percentage change on average of
the portfolio for every 1 percent change in the general
marke...
 We know how to measure risk, using standard deviation for
overall risk and beta for market risk.
 We know how to reduce...
 This linear relationship between risk and required return is
known as the Capital Asset Pricing Model (CAPM).
 CAPM equ...
 The Security Market Line (SML) is a graphic representation
of the CAPM, where the line shows the appropriate required
ra...
 Risk-Free Rate: This is the required rate of return or discount
rate for risk-less investments. Risk-free rate is typica...
CAPM
Example: ABC Corporation wishes to determine the required return on asset
Z, which has a beta of 1.5. The risk-free r...
REQUIRED RATE OF RETURN - CAPM
 Investor’s required rate of returns is the minimum rate of
return necessary to attract an...
Required
rate of
return
32
.
(7%)
Risk-
free
rate of
return
Beta
13%
1.5
(SML)
This linear relationship
between risk and r...
Ff topic4 risk_and_return
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Ff topic4 risk_and_return

  1. 1. Topic 4 Risk and Return
  2. 2. Learning Objectives  Define risk and return.  Identify risk and return relationship.  Calculate expected return and standard deviation.  Measure coefficient of variation.  Distinguish the different types of investment risks and methods that is used to measure them.  Explain portfolios and risk diversification.  Calculate required rate of return based on CAPM.
  3. 3. Return represents the total gain or loss on an investment. You invested in 1 share of Apple (AAPL) for $95 and sold a year later for $200. The company did not pay any dividend during that period. What will be the cash return on this investment? Cash Return = $200 + 0 - $95 = $105 Rate of Return = ($200 + 0 - $95) ÷ 95 = 110.53% Return
  4. 4. Expected return is what you expect to earn from an investment in the future. It is estimated as the average of the possible returns, where each possible return is weighted by the probability that it occurs. Where: Pb1 = probability of occurrence of the outcome r = return for the outcome n = number of outcomes considered Expected Return (k^ ) the return that an investor expects to earn on an asset, given its price, growth potential, etc. ‡Required Return ( k- ) the return that an investor requires on an asset given its risk and market interest rates. •This expected rate of return is in the form of cash flow. In referring to that, we will use cash flows in order to measure rate of return.
  5. 5. • Risk is defined as the chance of suffering a financial loss. Or the potential variability in future cash flows. • Risk may be used interchangeably with the term uncertainty to refer to the variability of returns (possible outcomes). •The wider the range of possible future events that can occur, the greater the risk. • Potential variability in future cash flow The possibilityʹ that an actual return will differ from our expected return. • A greater chance of loss are considered more risky than those with a lower chance of loss. Risk
  6. 6. Relationship between risk and return
  7. 7. • Standard deviation (S.D.) is one way to measure risk. It measures the volatility or riskiness of returns. (σ -sigma) • S.D. = square root of the weighted average squared deviation of each possible return from the expected return. This variability in returns can be quantified by computing the Variance or Standard Deviation in investment returns. the standard deviation, σk, which measures the dispersion around the expected value. Measurement Risk
  8. 8. State of Probability Return Economy (P) Company A Company B Recession 0.20 4% -10% Normal 0.50 10% 14% Boom 0.30 14% 30% k (A) = .2 (4%) + .5 (10%) + .3 (14%) = 10% k (B) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14% Based only on your expected return calculations, which stock would you prefer? Have you considered risk??????????
  9. 9. Company A ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46% Company B (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0 (30% - 14%)2 (.3) = 76.8 Variance = 192 Stand. dev. = 192 = 13.86% Company A company B Expected Return 10% 14% Standard Deviation 3.46% 13.86% Which company is good. It depends on your tolerance for risk! We can conclude that, company A has lower risk compared to investment B BUT Company B has higher return. Remember, there’s a tradeoff between risk and return. Example
  10. 10. The coefficient of variation, CV, is a measure of relative dispersion that is useful in comparing risks of assets with differing expected returns. CV = σ / k The higher the CV, the higher the risk. CV A = 3.46 % / 10% = 0.346 CV B = 13.86% / 14% = 0.99 A unit of risk in return for asset B is higher than asset A. As a conclusion, asset A is less risky than asset B. In comparing risk, it is more effective if we are using CV because it’s consider the relative size or the rate of return.
  11. 11. Return Measurement for a Single Asset: Expected Return (cont.)
  12. 12. Risk Measurement for a Single Asset: Standard Deviation (cont.) Table 1 The Calculation of the Standard Deviation of the Returns for Assets A and B
  13. 13. • An investment portfolio is any collection or combination of financial assets. • If we assume all investors are rational and therefore risk averse, that investor will ALWAYS choose to invest in portfolios rather than in single assets. •Investors will hold portfolios because he or she will diversify away a portion of the risk that is inherent in “putting all your eggs in one basket.” • If an investor holds a single asset, he or she will fully suffer the consequences of poor performance. • This is not the case for an investor who owns a diversified portfolio of assets. Portfolio and Diversification
  14. 14. ‡ Portfolio: Hold /Invest in different types of assets (or investments) at the same time or period.  Combining several securities in a portfolio can actually reduce overall risk. ‡ Example Invest in different type of securities may lower the risk of losses. This is because, if we loss in security B, probably, for security A we will earn profit. ‡Reduction in risk through investing in securities that NOT perfectly correlated. (assets with a negative correlation) Portfolio and Diversification
  15. 15.  Diversification: spreading out of investments to reduce risks. ‡ Investments across different securities rather than invest in only one stock. ‡ Reducing a risk of portfolio is depends on the correlation (r) between all of the stocks. ‡Correlation is a statistical measurement of the relationship between two variables. Positive Correlation Negative Correlation Possible correlations range from +1 to 1ʹ Diversification
  16. 16. ‡ If two stocks are perfectly positively correlated, diversification has NO effect on risk. i.e If correlation (r) = +1, we cannot abolish all the risk. A correlation of +1 indicates a perfect positive correlation, meaning that both stocks move in the same direction together. ‡ If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified. i.e If correlation (r) = -1, we can abolish the risk. A correlation of -1 indicates a perfect negative correlation, meaning that as one stock goes up, the other goes down. Diversification
  17. 17.  Investors should NOT expect to eliminate all risk from their portfolio. Some risk can be diversified away and some cannot.  Market risk (systematic risk) is nondiversifiable. This type of risk cannot be diversified away. Such as Unexpected changes in interest rates. Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.  Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification. Such as A company’s labor force goes on strike. A company’s top management dies in a plane crash. A huge oil tank bursts and floods a company’s production area. Investment risks
  18. 18. Investment risks
  19. 19.  Market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market. ƒ Proxy can be used as a market portfolio such as S&P 500 Index in the U.S and Nikkei 225 Index in Japan. ƒ In Malaysia, Bursa Malaysia (formerly known as KLSE) is one of the proxies that can be used as market portfolio. ƒ The movement in these indexes act as a benchmark to the movement of the market. Market portfolio
  20. 20.  Systematic risk called non-diversifiable risk because it is beyond the control of the investor and the firm. ƒ Systematic risk reflects mainly macroeconomic shocks that affect aggregate behavior of the economy. ƒ Market risk measured by beta (β = 1)  Once the asset return and market return obtained, a graph is prepare to see the relationship between asset return and market return. ƒ Asset return and market return are plot on Y-X-axis. ƒ When all the returns are plotted, draw a line of best-fit through coordinate point (0,0), which we call Characteristic line. Measuring market risk
  21. 21. Market returns and assets returns for certain period can be determined by looking at the percentage of changes in index or price based on the following equation: kt = (Pt / Pt – 1) – 1 Asset Return & Market Return Asset Market Period Price Return Index Return 0 19.00 853.42 1 19.29 1.53% 869.10 1.84% 2 20.90 8.34% 900.67 3.63% 3 19.54 -6.51% 901.89 0.14% 4 21.50 10.03% 923.80 2.42% Measuring return
  22. 22.  The slope of the line (beta), represents the average movement of the firm’s stock returns in response to a movement in the market’s return i.e the average relationship between a stock’s return and market’s returns.  Interpreting beta ( )ɴ A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market. A firm with a beta >1 is more volatile than the market. A firm with a beta < 1 is less volatile than the market. A firm with a beta=0 has no systematic risk. ¾ Most stocks have betas between 0.60 and 1.60 Measuring market risk
  23. 23.  Beta is a measure of how an individual stock’s returns vary with market returns.  Beta measures of the sensitivity of an individual stock’s return to changes in the market. It indicates the average response of a stock’s return to the change in the market as a whole. ƒ Example β = 1.2 means any increase/decrease by 1% in market return will cause an increase or decrease by 1.2% in asset return. Market risk
  24. 24. Portfolio beta indicates the percentage change on average of the portfolio for every 1 percent change in the general market. The portfolio beta is a weighted average of the individual asset's beta and assets has its own beta. β portfolio= Σ wj*βj Where wj = % invested in stock j βj = Beta of stock j Measuring portfolio beta
  25. 25.  We know how to measure risk, using standard deviation for overall risk and beta for market risk.  We know how to reduce overall risk to only market risk through diversification.  We need to know how much extra return we should require for accepting extra risk. What is the Required Rate of Return? The return on an investment required by an investor given market interest rates and the investment’s risk. ƒ The minimum rate of return necessary to attract an investor to purchase or hold a security. ƒ The required return for all assets is composed of two parts: the risk-free rate which is usually estimated from the return on treasury bills and a risk premium which is a function of both market conditions and the asset itself. Required Rate of Return (CAPM)
  26. 26.  This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM).  CAPM equation equates the required rate of return on a stock to the risk-free rate plus a risk premium for the systematic risk. The equation indicates that investor’s minimum acceptable rate of return is equal to the risk-free rate plus a risk premium for assuming risk. Required Rate of Return (CAPM)
  27. 27.  The Security Market Line (SML) is a graphic representation of the CAPM, where the line shows the appropriate required rate of return for a given stock’s systematic risk. CAPM- SML
  28. 28.  Risk-Free Rate: This is the required rate of return or discount rate for risk-less investments. Risk-free rate is typically measured by U.S. Treasury bill rate.  Risk Premium: Additional return we must expect to receive for assuming risk. As the level of risk increases, we will demand additional expected returns.  The risk premium for a stock is composed of two parts: The Market Risk Premium which is the return required for investing in any risky asset rather than the risk-free rate.  Beta, a risk coefficient which measures the sensitivity of the particular stock’s return to change in market conditions. CAPM- SML
  29. 29. CAPM Example: ABC Corporation wishes to determine the required return on asset Z, which has a beta of 1.5. The risk-free rate of return is 7%; the return on the market portfolio of assets is 11%. K Z = 7% + 1.5 [11% - 7%] = 13% According to the CAPM, Asset Z should be priced to give a 13% return.
  30. 30. REQUIRED RATE OF RETURN - CAPM  Investor’s required rate of returns is the minimum rate of return necessary to attract an investor to purchase or hold a security.  The required return for all assets is composed of two parts: the risk-free rate and a risk premium. The risk-free rate (Rf) is usually estimated from the return on treasury bills The risk premium is a function of both market conditions and the asset itself.
  31. 31. Required rate of return 32 . (7%) Risk- free rate of return Beta 13% 1.5 (SML) This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM). SML – The line that reflect the attitude of investors regarding the minimal acceptable return for a given level of systematic risk. 11% 1.0 Risk Premium Market Risk Premium Risk Free Rate

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