Topic 4Risk and Return

Learning ObjectivesDefine 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.

**

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

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 outcomer = return for the outcomen = 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.

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 possibility 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

Relationship between risk and return

Standard deviation (S.D.) is one way to measure risk. It measures the volatility or riskiness of returns. ( -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, k, which measures the dispersion around the expected value.

Measurement Risk

State of Probability ReturnEconomy (P) Company A Company BRecession 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??????????

Company A( 4% - 10%)2 (.2) = 7.2(10% - 10%)2 (.5) = 0(14% - 10%)2 (.3) = 4.8Variance = 12Stand. dev. = 12 = 3.46%Company B(-10% - 14%)2 (.2) = 115.2(14% - 14%)2 (.5) = 0(30% - 14%)2 (.3) = 76.8Variance = 192Stand. dev. = 192 = 13.86%

Company A company BExpected 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, theres a tradeoff between risk and return.Example

The coefficient of variation, CV, is a measure of relative dispersion that is useful in comparing risks of assets with differing expected returns.CV = / k

The higher the CV, the higher the risk.

CV A = 3.46 % / 10% = 0.346 CV B = 13.86% / 14% = 0.99A 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 its consider the relative size or the rate of return.

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 Deviationof the Returns for Assets A and B

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

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.

ExampleInvest 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

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 CorrelationNegative CorrelationPossible correlations range from +1 to 1Diversification

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

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 companys labor force goes on strike.A companys top management dies in a plane crash.A huge oil tank bursts and floods a companys production area.Investment risks

Investment risks

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. Proxy can be used as a market portfolio such as S&P 500 Index in the U.S and Nikkei 225 Index in Japan. In Malaysia, Bursa Malaysia (formerly known as KLSE) is one of the proxies that can be used as market portfolio. The movement in these indexes act as a benchmark to the movement of the market.

Market portfolio

Systematic risk called non-diversifiable risk because it is beyond the control of the investor and the firm. Systematic risk reflects mainly macroeconomic shocks that affect aggregate behavior of the economy. Market risk measured by beta ( = 1) Once the asset return and market return obtained, a graph is prepare to see the relationship between asset return and market return. Asset return and market return are plot on Y-X-axis. 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

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) 1Asset Return & Market Return Asset Market Period Price Return Index Return0 19.00 853.421 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

The slope of the line (beta), represents the average movement of the firms stock returns in response to a movement in the markets return i.e the average relationship between a stocks return and markets returns. Interpreting beta ()

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. Most stocks have betas between 0.60 and 1.60Measuring market risk

Beta is a measure of how an individual stocks returns vary with market returns. Beta measures of the sensitivity of an individual stocks return to changes in the market.

It indicates the average response of a stocks return to the change in the market as a whole.

Example = 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

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.

portfolio= wj*j Where wj = % invested in stock j j = Beta of stock jMeasuring portfolio beta

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 investments risk. 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 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)

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 investors minimum acceptable rate of return is equal to the risk-free rate plus a risk premium for assuming risk.

Required Rate of Return (CAPM)

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 stocks systematic risk.

CAPM- SML

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 stocks return to change in market conditions.

CAPM- SML

CAPMExample: 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.

REQUIRED RATE OF RETURN - CAPMInvestors 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 billsThe risk premium is a function of both market conditions and the asset itself.

Requiredrate of return

*.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 PremiumMarket Risk PremiumRisk Free Rate

WF1013/Asas/GroupB/Shafie/BAB6

**

WF1013/Asas/GroupB/Shafie/BAB6