risk and rate of return

TOPIC: RISK AND RATE OF RETURN

PREPARED BY: Mr. Hong Ry, MBA

Table of Content

I. INTRODUCTION .................................................................................................................... 1

II. RISK, INFLATION, RATES OF RETURN, AND THE FISHER EFFECT ................................ 1

1. Risk ............................................................................................................................................ 1 2. Inflation ...................................................................................................................................... 1 3. Rate of return ............................................................................................................................. 1 4. Interest rate ................................................................................................................................. 2 5. Real interest rate ........................................................................................................................ 3 6. Nominal interest rate .................................................................................................................. 3 7. Fisher Effect ............................................................................................................................... 3

III. TERM OF STRUCTURE OF INTEREST RATES ................................................................... 4

IV. THE RETURN AND RISK FOR PORTFOLIOS ...................................................................... 4

1. Return for Portfolios ...................................................................................................................... 5 2. Measuring Risk The Standard Deviation ....................................................................................... 5 3. Portfolio Risk ................................................................................................................................. 6 4. Diversification ............................................................................................................................... 7 5. Unique Risk and Market Risk ....................................................................................................... 8 6. The Concept of Beta ...................................................................................................................... 9

V. REQUIRED/EXPECTED RATE OF RETURN ....................................................................... 10

1. Capital Asset Pricing Model (CAMP) ......................................................................................... 10 2. Security Market Line (SML) ....................................................................................................... 11

VI. CONCLUSION ..................................................................................................................... 12

VII.REFERENCES ...................................................................................................................... 12

MBA Corporate Finance

Risk and Rate Of Return -1-

I. INTRODUCTION Generally, investors invest their fund with expecting to generate higher return and lower risk. In fact Risk and return go together and directly related. As the risk level of an investment increases, the potential return usually increases as well. The theory of risk and return is that high risk with high return and low risk with low return. Anyways, the investors can minimize/managing risk for their investment through knowing how to measure, reduce, and price risk of their investment. II. RISK, INFLATION, RATES OF RETURN, INTEREST RATE, REAL

INTEREST RATE, NOMINAL INTEREST RATE, AND THE FISHER EFFECT 1. Risk

Risk is defined as the quantifiable likelihood of loss or less-than-expected returns or the possibility that an actual return will differ from our expected return or uncertainty in the distribution of possible outcomes Examples: currency risk, inflation risk, principal risk, country risk, economic risk, mortgage risk, liquidity risk, market risk, opportunity risk, income risk, interest rate risk, prepayment risk, credit risk, unsystematic risk, call risk, business risk, counterparty risk, purchasing-power risk, event risk.

2. Inflation The overall general upward price movement of goods and services in an economy, usually as measured by the Consumer Price Index and the Producer Price Index. Over time, as the cost of goods and services increase, the value of a dollar is going to fall because a person won't be able to purchase as much with that dollar as he/she previously could. While the annual rate of inflation has fluctuated greatly over the last half century, ranging from nearly zero inflation to 23% inflation, the Fed actively tries to maintain a specific rate of inflation, which is usually 2-3% but can vary depending on circumstances. opposite of deflation.

3. Rate of return - Rate of return is income you collect on an investment expressed as a percentage of the

investment's purchase price. With a common stock, the rate of return is dividend yield, or your annual dividend divided by the price you paid for the stock.

In securities, the amount of revenue an investment generates as a percentage of the amount of capital invested over a given period of time. The rate of return shows the amount of time it will take to recover one's investment. For example, if one invests $1,000 and receives $150 in the first year of the investment, the rate of return is 15%, and the investor will recover his/her initial $1,000 in six years and eight months. Different investors have different required rates of return at different levels of risk.

With a bond, rate of return is the current yield, or your annual interest income divided by the price you paid for the bond. For example, if you paid $900 for a bond with a par value of $1,000 that pays 6% interest, your rate of return is $60 divided by $900, or 6.67%.

- Simple rate of return/Accounting rate of return is the measure of profitability

obtained by dividing the expected future annual net income by the required investment; also called Accounting Rate of Return or unadjusted rate of return. Sometimes the average investment rather than the original initial investment is used as the required investment, which is called average rate of return. Its formula:

Simple rate of return = Incremental revenues − Incremental expenses, including depreciation



= Incremental net operating income / Initial investment*]

Simple Return Calculation = t

tt

PPP −+1 or 11 −+

t

t

PP

Where 1+tP : the amount received tP : the amount invested

Example: You invested $50 at year t and you sold it at year t + 1 for $60. So simple return calculation as below:

Simple Return Calculation = t

tt

PPP −+1 or 11 −+

t

t

PP

= 50

5060 − = 20%

Or = 15060

− = 20%

4. Interest rate

A rate is charged or paid for the use of money. An interest rate is often expressed as an annual percentage of the principal. Simple Interest: I = Prt Where I: Amount of interest

P: principal r: interest rate t: period of time

Example: Alan borrowed $1,000 at a 6% annual interest rate for 8 months. So The 8-months total interest was calculated as below:

I = $1,000 x 0.06 x 128 = $40

Compound Interest: A = P(1 + r)t

Where A is the amount of money accumulated after n years, including interest P is the principal (the initial amount you borrow or deposit) r is the annual rate of interest (percentage) n is the number of years the amount is deposited or borrowed for.

Example: Alan borrowed $1,000 at a 6% annual interest rate for 8 months. So amount of money accumulated after 8 months, including interest, was calculated as below:

A = 8)1206.01(000,1$ + = $1, 040.70 or $ 40.70 (the 8-months total interest repayment)



The interest owed when compounding is taken into consideration is higher, because interest has been charged monthly on the principal + accrued interest from the previous months. For shorter time frames, the calculation of interest will be similar for both methods. As the lending time increases, though, the disparity between the two types of interest calculations grows.

5. Real interest rate

The nominal current interest rate minus the rate of inflation. For example, an investor is holding a 10% certificate of deposit during a period of 6% annual inflation. So investor would earn a real interest rate of 4%. The real interest rate is a more valid measure of the desirability of an investment than the nominal rate is.

6. Nominal interest rate

The stated interest rate on the face of a debt security or loan. For example, if a bond having a face value of $100,000 has a coupon interest rate of 8%, the nominal interest is $8000, which will be paid each year. The terms nominal interest rateand coupon rate are synonymous in discussing bonds; the latter term is still commonly used even though it is rare these days for bonds to be issued with physical coupons. For investment, the nominal interest rate refers to the stated rate of interest on an investment or security, before/without adjusting for inflation or inflationary expectations, as opposed to real interest rates. The real rate of interest is equal to the nominal rate less inflation.

7. Fisher Effect The effect proposes that if the real interest rate is equal to the nominal interest rate minus the expected inflation rate, and if the real interest rate were to be held constant, that the nominal rate and the inflation rate have to be adjusted on a one-for-one basis. This is known as the “Fisher Effect”. In simple terms: an increase in inflation will result in an increase in the nominal interest rate. For example, if the real interest rate is held at a constant 5.5% and inflation increased from 2% to 3%, the Fisher Effect indicates that the nominal interest rate would have to increase from 7.5% (5.5% real rate + 2% inflation rate) to 8.5% (5.5% real rate + 3% inflation rate).

krf ≈ k* + IRP or (1 + krf) = (1 + k*) (1 + IRP)

Where krf is nominal risk-free Interest Rate/nominal interest rate

k* is Real risk-free Interest Rate/real interest rate IRP is Inflation-risk premium/ inflation rate

Note: krf = k* + IRP is for approximation equal. The approximation works best when both the inflation rate and the real rate are small and when they are not small, throw the approximation away and do it right.

Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium?

(1 + krf) = (1 + k*) (1 + IRP) (1.08) = (1.03) (1 + IRP) (1 + IRP) = (1.0485), so IRP = 4.85%

Approximation krf ≈ k* + IRP

and IRP ≈ krf - k* IRP ≈ 0.08 – 0.03



IRP ≈ 0.05 or 5% III. TERM OF STRUCTURE OF INTEREST RATES The relationship between long-term and short-term interest rates especially on bond or long term date. (i.e., the relationship between and interest rate and the maturity on a security assuming everything else remains the same). The theory of term structure of interest rates is usually actually based on the relationship between interest rate on zero coupon bonds and the maturity of those bonds. And long-term coupon bonds can be looked at as a series of zero coupon bonds with different maturities.

Example: You can borrow $1,000 and lend at the same interest rate. Interest rate on a 2 year loan is 10%. And then you lend it at interest rate of 9.5% on 1-year loan starting from now and at interest rate of 11% on 1-year loan starting 1 year from now. Revenue from 2-years lending : $1,000 (1+9.5%)(1+11%) = $1,215.45 Loan Payback for 2-years : $1,000 (1+10%)2 = $1,210 Profit : $1,215 - $1,210 = $5.45 Although, the yield curve may be downward sloping or “inverted” if rates are expected to fall.

IV. THE RETURN AND RISK FOR PORTFOLIOS



1. Return for Portfolios The expected return on a portfolio ( r p ) is simply the weighted average return of the individual assets in the portfolio, the weights being the fraction of the total funds invested in each asset:

rp = w1 r1 + w2 r2 + ……….+ wn rn = ∑=

n

jj

1jr w

Where ri = expected return on each individual asset

wj = fraction for each respective asset investment n = number of assets in the portfolio

∑=

n

jj

1

w = 1.0

EXAMPLE: If the investor with $100 invests $60 in stock A with expected return 17.5% and $40 stock B with expected return 5.5%. What is the expected return on the portfolio?

Expected return on portfolio = ∑=

n

jj

1jr w = rp ; ∑

=

n

jj

1

w = 60/100 + 40/100 = 1

= ∑=

n

j 1

5.5%) x 17.5%)(0.4 x (0.6

= 12.7%

2. Measuring Risk The Standard Deviation The standard deviation (σ) is a measure of dispersion of the probability distribution, is commonly used to measure risk. The smaller the standard deviation, the tighter the probability distribution and, thus, the lower the risk of the investment.

Mathematically,

σ = i

n

ti

prr 2)(∑=

−

To calculate U, take the following steps: Step1. Compute the expected rate of return ( r ). Step2. Subtract each possible return from r' to obtain a set of deviations (ri- r ). Step3. Square each deviation; multiply the squared deviation by the probability of occurrence

for its respective return, and sum these products to obtain the variance (σ 2):

σ 2 = i

n

tiprr 2)(∑

=

−

Step 4. Finally, take the square root of the variance to obtain the standard deviation (σ ).



Example:

State of Economy Probability (P)

Return Orl. Utility Orl. Technology

Recession Normal Boom

.20

.50

.30

4% 10% 14%

-10% 14% 30%

Orl. Utility

Return ( ri)( %) Probability (pi) Step 1 rip(%)

Step 2 rr −( )(%)

Step 3

rr −( )2 rr −( )2pi(%)

4% 10% 14%

.20

.50

.30

0.8 5

4.2

-6 0 4

36 0

16

7.2 0

4.8 r = 10 Variance = 12 σ = 12 = 3.46%

Orl.Technology

Return ( ri)( %) Probability (pi) Step 1 rip(%)

Step 2 rr −( )(%)

Step 3

rr −( )2 rr −( )2pi(%)

-10% 14% 30%

.20

.50

.30

-2 7 9

-24 0 16

576 0

256

115.2 0

76.8 r = 14 Variance = 192 σ = 192 = 13.95%

Orl. Utility Orl. Technology Expected return( r ) Standard deviation (σ)

10% 3.46%

14% 13.86%

σ/ r 34.6% 99%

Although Orl. Technology is expected to produce a considerably higher return than Orl. Utility, Orl. Technology is overall more risky than Orl. Utility, based on the computed coefficient variation, because Orl. Technology has greater Standard deviation up to 13.86% while its expected return is only 14%.

3. Portfolio Risk Unlike returns, the risk of a portfolio (σP) is not simply the weighted average of the standard deviations of the individual assets in the contribution, for a portfolio’s risk is also dependent on the correlation coefficients of its assets. The correlation coefficient ( p ) is a measure of the degree to which two variables “move” together. It has a numerical value that ranges from -1.0 to 1.0. In a two-asset (A and B) portfolio, the portfolio risk is defined as:

σP = BAA ww σσσσ ABBAB

2B

22A

2 p * w2w ++

Where σA and σB = standard deviations of assets A and B, respectively wA and wB = weights, or fractions, of total funds invested in assets A and B pAB = the correlation coefficient between assets A and B



Portfolio is combining several securities in a portfolio can actually reduce overall risk by choosing to hold a portfolio of several stocks instead of holding individual stock which pertain the higher risk.

4. Diversification An investment strategy designed to reduce risk by spreading the funds invested across many securities. Since people hold diversified portfolios of securities, they are not very concerned about the risk and return of a single security. They are more concerned about the risk and return of their entire portfolio. Portfolio risk can be minimized by diversification, or by combining assets in an appropriate manner. The degree to which risk is minimized depends on the correlation between the assets being combined. For example, by combining two perfectly negative correlated assets (p = - l), the overall portfolio risk can be completely eliminated. Combining two perfectly positive correlated assets (p = +1) does nothing to help reduce risk. An example of the latter might be ownership of two automobile stocks or two housing stocks. EXAMPLE: Assume the investor with $120 invests $40 in stock A with risk of stock A (σA )

20% and $80 stock B with risk of stock B (σB) 20%.

Asset σ w A 20% 1/3 B 10% 2/3

The portfolio risk then is:

σP = BAA ww σσσσ ABBAB2

B22

A2 p * w2w ++

= )1.0)(2.0(p *)32)(

31(2 )1.0()

32( )2.0()

31( AB

2222 ++

= ABp 0.00890.0089 +

a) Now assume that A and B is a perfectly positive correlation. It means that when the value of asset A increases and value of asset B increase as well. In contrary, when value of asset A decreases the value of asset B also decrease. The portfolio risk when p = +1 then becomes



σP = ABp 0.00890.0089 + = (1) 0.00890.0089 + = 0.0178 =13.34% b) If p = 0, the assets lack correlation and the portfolio risk is simply the risk of the expected

returns on the assets, i.e., the weighted average of the standard deviations of the individual assets in the portfolio. Therefore, when PAB = 0, the portfolio risk for this example is:

σP = ABp 0.00890.0089 + = (0) 0.00890.0089 + = 0.0089 = 9.43%

c) If p = -1 (a perfectly negative correlation coefficient), then as the price of A rises, the price of B declines at the very same rate. In such a case, risk would be completely eliminated. Therefore, when PAB = -1, the portfolio risk is

σP = ABp 0.00890.0089 + = (-1) 0.00890.0089 + = 0 = 0

When we compare the results of (a), (b), and (c), we see that a positive correlation between assets increases a portfolio’s risk above the level found at zero correlation, while a perfectly negative correlation eliminates that risk.

5. Unique Risk and Market Risk - Unique Risk also called “diversifiable risk” and “unsystematic risk.” The part of a security’s

risk associated with random outcomes generated by events specific to the firm. This risk can be eliminated by proper diversification.

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

- Market Risk also called “systematic risk.” The part of a security’s risk that cannot be eliminated by diversification because it is associated with economic or market factors that systematically affect most firms and, hence, overall stock market.

Unexpected changes in interest rates. Unexpected changes in cash flows due to tax rate changes, foreign competition, and the

overall business cycle Anyways, some firms have more market risk than others. For instant, Interest rate changes affect all firms, but which would be more affected commercial banks.

Note: As we know, the market compensates investors for accepting risk - but only for market risk. Company-unique risk can and should be diversified away. So, we need to be able to measure market risk. Also, investors holding diversified portfolios are mostly concerned with



macroeconomic risks. They do not worry about microeconomic risks peculiar to a particular company or investment project. Micro risks wash out in diversified portfolios. Company managers may worry about both macro and micro risks, but only the former affect the cost of capital.

6. The Concept of Beta The market, or systematic, risk can be measured by comparing the return on an investment with the return on the market in general, or an average stock; the resulting measure is called the beta coefficient, and is identified using the Greek symbol β; graphically, β can be determined as follows:

The beta coefficient shows how the returns associated an investment move with respect to the returns associated the market; because the market is very well diversified, its returns should be affected by systematic risk only—unsystematic risk should be completely diversified away in a portfolio that contains all investments in the market; thus, the beta coefficient is a measure of systematic risk because it gives an indication of the degree of movement in returns associated with an investment relative to the market, which contains only systematic risk.

nnp www ββββ +++= ........2211

∑=

n

j 1jj )(w β

Where β represents the beta coefficients and Wj is the percent of the total amount invested in the portfolio that is invested in Investment j.

Example: Consider the following portfolio:

Investment Beta Amount Invested Stock A 2.5 $ 10,000 Stock B 1.2 25,000 Stock C 1.8 35,000 Stock D 0.5 30,000

$100,000

)000,100$000,30$(5.0)

000,100$000,35$(8.1)

000,100$000,25$(2.1)

000,100$000,10$(5.2 +++=pβ

= 2.5 (0.10) + 1.2 (0.25) + 1.8 (0.35) + 0.5 (0.30) = 1.33



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. For instant, technology firms. And

if β = 2.0 generally is considered twice as risky as the market, such that the risk premium associated with the investment should be twice the risk premium on the market.

A firm with a beta = 0 is generally is considered riskless /risk free on the market. For example, Treasury bills.

A firm with a beta < 1 is less volatile than the market. For example, utilities firms. V. REQUIRED/EXPECTED RATE OF RETURN

The minimum rate of return that an investment must provide, or must be expected to provide, in order to justify its acquisition. For example, an investor who can earn an annual return of 5% on certificates of deposit may set a required rate of return of 9% on a more risky stock investment before considering a shift of funds into the stock. An investment's required rate of return is a function of the returns available on other investments and the risk level inherent in a particular investment. The relationship between risk and expected return on a security is measured by capital asset pricing model (CAPM). The model, also called the security market line security market line (SML).

1. Capital Asset Pricing Model (CAMP) Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.

The commonly used formula to describe the CAPM relationship is as follows: Required (or expected) Return = RF Rate + (Market Return - RF Rate)*Beta

For example, let's say that the current risk free-rate is 6%, and the S&P 500 is expected to return to 12% next year. You are interested in determining the return that Joe's Oyster Bar Inc (JOB) will have next year. You have determined that its beta value is 1.2. The overall stock market has a beta of 1.0, so JOB's beta of 1.2 tells us that it carries more risk than the overall market; this extra risk means that we should expect a higher potential return than the 12% of the S&P 500. We can calculate this as the following: Required (or expected) Return = 6% + (12% - 6%)*1.2 Required (or expected) Return = 13.2%

This calculation tells us is that Joe's Oyster Bar has a required rate of return of 13.2%. So, if you invest in JOB, you should be getting at least 13.2% return on your investment. If you don't think that JOB will produce those kinds of returns for you, then you should consider investing in a different company. It is important to remember that high-beta shares usually give the highest returns. Over a long period of time, however, high beta shares are the worst performers during market declines (bear markets). While you might receive high returns from high beta shares, there is no guarantee that the CAPM return is realized.



2. Security Market Line (SML) The security market line shows how expected rate of return depends on beta. According to the capital asset pricing model, expected rates of return for all securities and all portfolios lie on this line.

The SML essentially graphs the results from the capital asset pricing model (CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. The market risk premium is determined from the slope of the SML. The security market line is a useful tool in determining whether an asset being considered for a portfolio offers a reasonable expected return for its risk. Individual securities are plotted on the SML graph. If a security's risk versus expected return is plotted above the SML, it is undervalued because the investor can expect a greater return for the inherent risk. A security plotted below the SML is overvalued because the investor would be accepting less return for the amount of risk assumed.

Required return = risk-free rate of return + risk premium

r = rf + β (rm – rf)

Where r = the expected (or required) return on security j rf = the risk-free security (such as a T-bill) rm = the expected return on the market portfolio β = beta, an index of nondiversifiable (noncontrollable, systematic) risk β (rm – rf) = risk premium

EXAMPLE: Assuming that the risk-free rate ( rf ) is 8 percent, and the expected return for the

market (rm) is 12 percent, then if β = 1 (Market portfolio). Expected (required) rate of return ( r) = rf + β (rm – rf)

rj = 8% + 1.0 (12% -8%) = 12%



If the expected (required) rate of return plots below the SML, investment should be rejected because it is a negative-NPV investment. By the way, if expected rate of return plots above the SML, investment should be accepted.

VI. CONCLUSION The theory of risk and return is that high risk with high return and low risk with low return. Risk and rate of return illustrates the means to manage risk on investment and guide investors to make proper decision for their investments which offer reasonable expected return with taking acceptable risk. Total risk was divided into UNIQUE RISK which effects on specific to the firm and can be eliminated by proper diversification and MARKET RISK which systematically affect most firms and, hence, overall stock market and cannot be diversified. Further more investors can reduce risk for their investment by investing in portfolio securities (holding a portfolio of several stocks instead of holding individual stock which pertain the higher risk) and diversification strategy (spreading the funds invested across many securities). Risk can be measured by using standard deviation for overall risk. The investments that have higher standard deviation, its risk is high. And beta is another method to measure market risk. A beta = 1 has average market risk. The stock is no more or less volatile than the market; beta > 1 is more volatile than the market (technology firms); beta = 0 is generally is considered riskless /risk free on the market. For example, Treasury bills; and beta < 1 is less volatile than the market (utilities firms). Capital asset pricing model (CAPM) shows the relationship between risk and expected return on a security and security market line (SML) shows how expected rate of return depends on beta. Capital asset pricing model (CAPM) and security and security market line (SML) were used to pricing risk for investments. If the expected (required) rate of return plots below the SML, investment should be rejected because it is a negative-NPV investment. By the way, if expected rate of return plots above the SML, investment should be accepted. In real practice the investors often choose or accept to invest their fund in specific businesses that generate the higher return by depending on their tolerance for risk rather than focus on the expected investment risk. VII. REFERENCES

1. Schaum's Outline of Theory and Problems of Financial Management, second edition, 1998; JAE K. SHIM, Ph.D and JOEL. G. SIEGEL, Ph.D.CPA

2. Fundamentals of Corporate Finance Third Edition, 2001; Richard A. Brealey, Stewart C. Myers, Alan J. Marcus, and Wallace E. Carroll

3. Slides handouts from internet search_google_Cash flow analysis.ppt. 4. http://www.coba.usf.edu/departments/finance/faculty/besley/notes/risk.pdf

Expected rate of return below SML, investment should be rejected because NPV is negative.

Expected rate of return on or above SML, investment should be accepted because NPV is equal 0 or positive.



5. http://www.cbpa.ewu.edu/~deagle/f434/termstruc/sld003.htm 6. http://www.finance.google.com/

RISK AND RATE OF RETURNRISK AND RATE OF RETURN

Chapter 13: Risk and Chapter 13: Risk and ppRates of ReturnRates of Return

Return

2Risk

© 2002, Prentice Hall, Inc.

Chapter 13: ObjectivesChapter 13: Objectivesp jp j

Inflation and rates of returnInflation and rates of returnInflation and rates of returnInflation and rates of returnHow to How to measuremeasure risk risk (variance standard deviation(variance standard deviation(variance, standard deviation, (variance, standard deviation, beta)beta)How to How to reducereduce riskrisk(diversification)(diversification)( )( )How to How to priceprice riskrisk(security market line CAPM)(security market line CAPM)

3

(security market line, CAPM)(security market line, CAPM)

Inflation, Rates of Return, Inflation, Rates of Return, d th Fi h Eff td th Fi h Eff tand the Fisher Effectand the Fisher Effect

InterestRates

4

Conceptually:Interest Interest RatesRatesConceptually:

Nominal Real Inflation-

RatesRates

risk-freeInterest =

risk-freeInterest +

Inflationrisk

premiumRate krf

Rate k*

p e uIRP

Mathematically:

(1 + krf) = (1 + k*) (1 + IRP)

5This is known as the “Fisher Effect”

Interest Interest RatesRates

Suppose the real rate is 3%, and the Suppose the real rate is 3%, and the

RatesRates

nominal rate is 8%. What is the inflation nominal rate is 8%. What is the inflation rate premium?rate premium?

(1 + k(1 + krfrf) = (1 + k*) (1 + IRP)) = (1 + k*) (1 + IRP)(1 08) = (1 03) (1 + IRP)(1 08) = (1 03) (1 + IRP)(1.08) = (1.03) (1 + IRP)(1.08) = (1.03) (1 + IRP)

(1 + IRP) = (1.0485),(1 + IRP) = (1.0485),( ) ( ),( ) ( ),so IRP = 4.85%so IRP = 4.85%

6

Term Structure of Interest RatesTerm Structure of Interest RatesThe pattern of rates of return The pattern of rates of return for debt securities that differ for debt securities that differ only in the length of time to only in the length of time to maturity.maturity.

yieldto

maturitymaturity

ti t t it ( )7

time to maturity (years)

Term Structure of Interest RatesTerm Structure of Interest RatesThe yield curve may be downward The yield curve may be downward sloping or “inverted” if rates are sloping or “inverted” if rates are expected to fall.expected to fall.

yieldtoto

maturity

8

time to maturity (years)

For a Treasury security, For a Treasury security, what is the required ratewhat is the required ratewhat is the required rate what is the required rate

of return?of return?

RequiredRequiredt ft f

RiskRisk--freefreet ft frate of rate of

returnreturn== rate of rate of

returnreturnSince Treasuries are essentially free Since Treasuries are essentially free

of default risk the rate of returnof default risk the rate of returnof default risk, the rate of return of default risk, the rate of return on a Treasury security is on a Treasury security is

considered the “considered the “riskrisk--freefree” rate of” rate of9

considered the considered the riskrisk--freefree rate of rate of return.return.

For a For a corporate stock or bondcorporate stock or bond, what , what is the required rate of return?is the required rate of return?

RequiredRequired RiskRisk--freefree RiskRiskrate of rate of returnreturn

== ++rate of rate of returnreturn

premiumpremium

ff

returnreturn returnreturn

How large of a How large of a risk premiumrisk premium should should we require to buy a corporate we require to buy a corporate

ii10

security? security?

ReturnsReturns

Expected ReturnExpected Return -- the return the return ppthat an investor expects to that an investor expects to earn on an asset, given itsearn on an asset, given itsearn on an asset, given its earn on an asset, given its price, growth potential, etc.price, growth potential, etc.R i d R tR i d R t th tth tRequired ReturnRequired Return -- the return the return that an investor requires on an that an investor requires on an asset given itsasset given its riskrisk and market and market interest rates.interest rates.

11

Expected Expected ReturnReturnReturnReturn

State of Probability ReturnState of Probability ReturnyyEconomy (P) Economy (P) Orl. Utility Orl. TechOrl. Utility Orl. Tech

Recession .20 4%Recession .20 4% --10%10%Recession .20 4% Recession .20 4% 10%10%Normal .50 10% 14%Normal .50 10% 14%Boom .30 14% 30%Boom .30 14% 30%Boom .30 14% 30%Boom .30 14% 30%For each firm, the expected return on the stock For each firm, the expected return on the stock

is just ais just a weighted averageweighted average::is just a is just a weighted averageweighted average::

12

What is Risk?What is Risk?

Th ibilit th tTh ibilit th t t lt lThe possibility that an The possibility that an actualactualreturn will differ from our return will differ from our expectedexpected return.return.

U t i t i th di t ib tiU t i t i th di t ib tiUncertainty in the distribution Uncertainty in the distribution of possible outcomes.of possible outcomes.

13

What is Risk?What is Risk?Uncertainty in the distribution Uncertainty in the distribution yyof possible outcomes.of possible outcomes.

0.2

Company B0.5

Company A

0 060.080.1

0.120.140.160.18

0.150.2

0.250.3

0.350.4

0.45

returnreturn

00.020.040.06

-10 -5 0 5 10 15 20 25 300

0.050.1

4 8 12

returnreturn

14

returnreturnreturnreturn

How do we Measure Risk?How do we Measure Risk?

To get a general idea of aTo get a general idea of aTo get a general idea of a To get a general idea of a stock’s price variability, we stock’s price variability, we could look at thecould look at the stock’s pricestock’s pricecould look at the could look at the stock s price stock s price rangerange over the past year.over the past year.

52 weeks Yld Vol NetHi Lo Sym Div % PE 100s Hi Lo Close Chg134 80 IBM 52 5 21 143402 98 95 9549 3134 80 IBM .52 .5 21 143402 98 95 9549 -3

115 40 MSFT … 29 558918 55 52 5194 -475

15

115 40 MSFT … 29 558918 55 52 51 4

How do we Measure Risk?How do we Measure Risk?

A more scientific approach is toA more scientific approach is toA more scientific approach is to A more scientific approach is to examine the stock’s examine the stock’s standard standard deviationdeviation of returnsof returnsdeviationdeviation of returns.of returns.Standard deviation is a measure of Standard deviation is a measure of thethe dispersion of possibledispersion of possiblethe the dispersion of possible dispersion of possible outcomesoutcomes. . Th t th t d d d i tiTh t th t d d d i tiThe greater the standard deviation, The greater the standard deviation, the greater the uncertainty, and the greater the uncertainty, and th f th t th i kth f th t th i k

16

therefore , the greater the risk.therefore , the greater the risk.

Standard DeviationStandard DeviationStandard DeviationStandard Deviation

n

= (k= (kii -- k)k)22 P(kP(kii))σn

Σ (( )) (( ))σi=1Σ

17

= (ki - k)2 P(ki)σ n

Σ (ki k) P(ki)σi=1Σ

Orlando Utility, Inc. Orlando Utility, Inc. ( 4%( 4% -- 10%)10%)22 (.2) = 7.2(.2) = 7.2( 4% ( 4% 10%)10%) (.2) 7.2(.2) 7.2(10% (10% -- 10%)10%)22 (.5) = 0(.5) = 0(14%(14% 10%)10%)22 ( 3)( 3) 4 84 8(14% (14% -- 10%)10%)22 (.3)(.3) = = 4.84.8Variance Variance = 12= 12

18

Stand. dev. = 12 = Stand. dev. = 12 = 3.46%3.46%

(ki k)2 P(ki)σ n

Σ= (ki - k)2 P(ki)σi=1Σ

Orlando Technology, Inc. Orlando Technology, Inc. ((--10% 10% -- 14%)14%)22 (.2) = 115.2(.2) = 115.2(14%(14% -- 14%)14%)22 (.5) = 0(.5) = 0(14% (14% 14%)14%) (.5) 0(.5) 0(30% (30% -- 14%)14%)22 (.3)(.3) = = 76.876.8Variance = 192Variance = 192Variance = 192Variance = 192Stand. dev. = 192 = Stand. dev. = 192 = 13.86%13.86%

19

Which stock would you Which stock would you yyprefer?prefer?

H ld d id ?H ld d id ?How would you decide?How would you decide?

20

SummarySummary

Orlando OrlandoOrlando OrlandoO do O doO do O doUtilityUtility TechnologyTechnology

Expected ReturnExpected Return 10% 14%10% 14%

Standard DeviationStandard Deviation 3.46% 13.86%3.46% 13.86%

21

It depends on your tolerance for It depends on your tolerance for risk! risk!

Return

Remember, there’s a tradeoff Remember, there’s a tradeoff Risk

22

between risk and return.between risk and return.

PortfoliosPortfolios

Combining several Combining several securities in a portfolio securities in a portfolio ppcan actually can actually reduce reduce overall riskoverall risk..overall riskoverall risk..How does this work?How does this work?

23

Suppose we have stock A and stock B. The returns on these stocks do not tendThe returns on these stocks do not tend to move together over time (they are not perfectly correlated)not perfectly correlated).

kArateof

return kB

24time

What has happened to the i bilit f t f thvariability of returns for the

portfolio?

rate kpkA

rateof

return

p

kBreturn kB

25time

DiversificationDiversificationDiversificationDiversificationInvesting in more than one Investing in more than one security to reduce risksecurity to reduce risksecurity to reduce risk.security to reduce risk.If two stocks are perfectly If two stocks are perfectly

i i li i l l dl dpositivelypositively correlated, correlated, diversification has no effect on diversification has no effect on i ki krisk.risk.

If two stocks are perfectly If two stocks are perfectly negativelynegatively correlated, the portfolio correlated, the portfolio is perfectly diversified.is perfectly diversified.

26

If you owned a share of everyIf you owned a share of everyIf you owned a share of every If you owned a share of every stock traded on the NYSE and stock traded on the NYSE and NASDAQ would you beNASDAQ would you beNASDAQ, would you be NASDAQ, would you be diversified?diversified?YES!YES!Would you have eliminated allWould you have eliminated allWould you have eliminated all Would you have eliminated all of your risk?of your risk?NO!NO! C t k tf liC t k tf liNO!NO! Common stock portfolios Common stock portfolios still have risk. still have risk.

27

Some risks can be diversified Some risks can be diversified away and some cannot.away and some cannot.

Market riskMarket risk ((systematic risk)systematic risk) is is di ifi bldi ifi bl Thi f i kThi f i knondiversifiable. nondiversifiable. This type of risk This type of risk

cannot be diversified away.cannot be diversified away.CompanyCompany--unique riskunique risk(unsystematic risk)(unsystematic risk) is is diversifiablediversifiable. . This type of risk can be reduced This type of risk can be reduced through diversification.through diversification.

28

Market RiskMarket RiskMarket RiskMarket Risk

Unexpected changes in interest Unexpected changes in interest ratesratesrates.rates.Unexpected changes in cash Unexpected changes in cash fl d hfl d hflows due to tax rate changes, flows due to tax rate changes, foreign competition, and the foreign competition, and the overall business cycle.overall business cycle.

29

CompanyCompany--unique unique RiskRisk

’ l b f’ l b fA company’s labor force goes on A company’s labor force goes on strike.strike.A company’s top management A company’s top management dies in a plane crashdies in a plane crashdies in a plane crash.dies in a plane crash.A huge oil tank bursts and floods A huge oil tank bursts and floods a company’s production area.a company’s production area.

30

As you add stocks to your As you add stocks to your portfolio, companyportfolio, company--unique unique risk is reduced.risk is reduced.risk is reduced.risk is reduced.

portfolioriskrisk

companycompany-unique

risk

Market risk

risk

31number of stocks

Do some firms have more Do some firms have more

YesYes For example:For example:

market risk than others?market risk than others?YesYes.. For example:For example:Interest rate changes affect all Interest rate changes affect all

firms, but which would be firms, but which would be moremoreaffected:affected:

) R t il f d h i) R t il f d h ia) Retail food chaina) Retail food chainb) b) Commercial bankCommercial bank

32

))

NoteNoteNoteNoteAs we know, the market As we know, the market

t i t ft i t fcompensates investors for compensates investors for accepting risk accepting risk -- but only for but only for market riskmarket risk.. CompanyCompany--unique unique risk can and should be risk can and should be diversified away.diversified away.

So So -- we need to be able to we need to be able to

33

measuremeasure market risk.market risk.

This is why we haveThis is why we have Beta.Beta.This is why we have This is why we have Beta.Beta.

Beta: a measure of market risk.Beta: a measure of market risk.Beta: a measure of market risk.Beta: a measure of market risk.Specifically, beta is a measure of Specifically, beta is a measure of how an individual stock’s returnshow an individual stock’s returnshow an individual stock s returns how an individual stock s returns vary with market returns.vary with market returns.

It’s a measure of the It’s a measure of the “sensitivity”“sensitivity”of an individual stock’s returns toof an individual stock’s returns toof an individual stock s returns to of an individual stock s returns to changes in the market.changes in the market.

34

The market’s beta isThe market’s beta is 11

A firm that has aA firm that has a beta = 1beta = 1 hashas averageaverage

The market s beta is The market s beta is 11

A firm that has a A firm that has a beta = 1beta = 1 has has average average market riskmarket risk. The stock is no more or less . The stock is no more or less volatile than the market.volatile than the market.volatile than the market.volatile than the market.A firm with a A firm with a beta > 1beta > 1 is is more volatilemore volatilethan the market.than the market.than the market. than the market.

(ex: technology firms)(ex: technology firms)A firm with aA firm with a beta < 1beta < 1 isis less volatileless volatileA firm with a A firm with a beta < 1beta < 1 is is less volatileless volatilethan the market.than the market.

(ex: utilities)(ex: utilities)

35

(ex: utilities)(ex: utilities)

Calculating BetaCalculating BetaXYZ C

Beta = slope

15

XYZ Co. returns. . . = 1.20

10. . . .

. . . .. . . .5

S&P 500

. . . .. . . .

-5-15 5 10 15-10 -5returns . . . .

. . . .-10. . . .. . . .

. . . .

36

-15. . . .

Summary:Summary:

We know how toWe know how to measuremeasure risk, risk, ii t d d d i tit d d d i ti f llf llusing using standard deviationstandard deviation for overall for overall

risk and risk and betabeta for market risk.for market risk.We kno ho toWe kno ho to ed ceed ce o e all isko e all iskWe know how to We know how to reducereduce overall risk overall risk to only market risk through to only market risk through diversificationdiversificationdiversificationdiversification..We need to know how to We need to know how to priceprice risk risk so we will know how much extraso we will know how much extraso we will know how much extra so we will know how much extra return we should require for return we should require for accepting extra risk.accepting extra risk.

37

What is the Required Rate of What is the Required Rate of qqReturn?Return?

The return on an investment The return on an investment i d b i t ii d b i t irequired by an investor given required by an investor given

market interest rates and the market interest rates and the investment’s investment’s riskrisk..

38

Required Risk-free Riskrate of return

= +rate of return

premiumreturn return

marketrisk

company-i i krisk unique risk

b di ifi d39

can be diversifiedaway

This linear relationshipThis linear relationshipThis linear relationship This linear relationship between risk and required between risk and required

return is known as the return is known as the Capital Asset Pricing Capital Asset Pricing p gp g

ModelModel (CAPM).(CAPM).

40

RequiredRequiredrate of rate of

SMLIs there a riskless

returnreturnIs there a riskless(zero beta) security?

.12%TreasuryTreasury

securities arel i klas close to risklessas possible. Risk-free

rate ofrate ofreturn(6%)

41Beta10


SMLWhere does the S&P 500returnreturn fall on the SML?

.12%The S&P 500 is

a gooda good approximationfor the market

Risk-freerate of for the marketrate ofreturn(6%)

42Beta10


SMLreturnreturn

Utility

.12%

yStocks

Risk-freerate ofrate ofreturn(6%)

43Beta10


SMLHigh-techstocksreturnreturn stocks

.12%

Risk-freerate ofrate ofreturn(6%)

44Beta10

The CAPM equation:The CAPM equation:

kkjj = k= krfrf ++ jj (k(kmm -- kkrfrf ))

qq

βkkjj k krfrf + + jj (k(kmm kkrf rf ))

where:where:

β

kkjj = the required return on security j,= the required return on security j,

kk ff th i kth i k f t f i t tf t f i t tkkrfrf = the risk= the risk--free rate of interest,free rate of interest,

jj = the beta of security j, and = the beta of security j, and βjj y j,y j,

kkmm = the return on the market index.= the return on the market index.

45

Example:Example:pp

S th T b dS th T b dSuppose the Treasury bond Suppose the Treasury bond rate is rate is 6%6%, the average , the average return on the S&P 500 index return on the S&P 500 index is is 12%12%, and Walt Disney has , and Walt Disney has , y, ya beta of a beta of 1.21.2..According to the CAPM whatAccording to the CAPM whatAccording to the CAPM, what According to the CAPM, what should be the required rate should be the required rate

f Di k?f Di k?46

of return on Disney stock?of return on Disney stock?

kk = k= k + (k+ (k -- kk ))βkkjj = k= krfrf + (k+ (kmm -- kkrf rf ))kk 06 + 1 2 ( 1206 + 1 2 ( 12 06)06)

βkkjj = .06 + 1.2 (.12 = .06 + 1.2 (.12 -- .06).06)kkjj = .132 == .132 = 13.2%13.2%kkjj .132 .132 13.2%13.2%

According to the CAPM, According to the CAPM, Disney stock should beDisney stock should beDisney stock should be Disney stock should be priced to give a 13.2% priced to give a 13.2%

47

return.return.

RequireRequiredd

SMLTheoretically, every rate of rate of returnreturn

security should lie on the SML

.12% If every stockIf every stockis on the SML,

investors are being fullyinvestors are being fullycompensated for risk.Risk-free

rate ofrate ofreturn(6%)

48Beta10

RequireRequiredd

SMLIf a security is aboverate of rate of returnreturn

the SML, it isunderpriced.

.12%

p

If a security is below the SML, itbelow the SML, it

is overpriced.Risk-freerate ofrate ofreturn(6%)

49Beta10

Simple Return CalculationsSimple Return Calculations$50 $60

t t+1

= = = 20%= 20%PPt+1t+1 -- PPt t 60 60 -- 5050

PP 5050PPtt 5050

-- 11 = = --11 = 20%= 20%PPt+1t+1 6060PP 5050

50

PPtt 5050

SummarySummaryThe theory of risk and return is that high risk with high return and low riskThe theory of risk and return is that high risk with high return and low riskThe theory of risk and return is that high risk with high return and low risk The theory of risk and return is that high risk with high return and low risk with low return. Risk and rate of return illustrates the means to manage with low return. Risk and rate of return illustrates the means to manage risk on investment and guide investors to make proper decision for their risk on investment and guide investors to make proper decision for their investments which offer reasonable expected return with taking investments which offer reasonable expected return with taking acceptable risk.acceptable risk.Total risk for investment was divided into UNIQUE RISK which effects onTotal risk for investment was divided into UNIQUE RISK which effects onTotal risk for investment was divided into UNIQUE RISK which effects on Total risk for investment was divided into UNIQUE RISK which effects on specific to the firm and can be eliminated by proper diversification and specific to the firm and can be eliminated by proper diversification and MARKET RISK which systematically affect most firms and, hence, overall MARKET RISK which systematically affect most firms and, hence, overall stock market and cannot be diversified.stock market and cannot be diversified.Further more investors can reduce risk for their investment by investing in Further more investors can reduce risk for their investment by investing in

f li i i (h ldi f li f l k i d f h ldif li i i (h ldi f li f l k i d f h ldiportfolio securities (holding a portfolio of several stocks instead of holding portfolio securities (holding a portfolio of several stocks instead of holding individual stock which pertain the higher risk) and diversification strategy individual stock which pertain the higher risk) and diversification strategy (spreading the funds invested across many securities).(spreading the funds invested across many securities).Risk of investment can be measured by using standard deviation for Risk of investment can be measured by using standard deviation for overall risk. The investments that have higher standard deviation, its risk overall risk. The investments that have higher standard deviation, its risk o e a s e es e s a a e g e s a da d de a o , s so e a s e es e s a a e g e s a da d de a o , s sis high. And beta is another method to measure market risk. And good is high. And beta is another method to measure market risk. And good beta should be equal or lower than one.beta should be equal or lower than one.Capital asset pricing model (CAPM) shows the relationship between risk Capital asset pricing model (CAPM) shows the relationship between risk and expected return on a security and security market line (SML) shows and expected return on a security and security market line (SML) shows how expected rate of return depends on beta Investor can use Capitalhow expected rate of return depends on beta Investor can use Capitalhow expected rate of return depends on beta. Investor can use Capital how expected rate of return depends on beta. Investor can use Capital asset pricing model (CAPM) and security and security market line (SML) to asset pricing model (CAPM) and security and security market line (SML) to pricing risk for investments. If the expected (required) rate of return plots pricing risk for investments. If the expected (required) rate of return plots below the SML, investment should be rejected because it is a negativebelow the SML, investment should be rejected because it is a negative--NPV investment. By the way, if expected rate of return plots above the NPV investment. By the way, if expected rate of return plots above the SML, investment should be accepted.SML, investment should be accepted.

51

SML, investment should be accepted.SML, investment should be accepted.In real practice the investors often choose or accept to invest their fund in In real practice the investors often choose or accept to invest their fund in specific businesses that generate the higher return by depending on their specific businesses that generate the higher return by depending on their tolerance for risk rather than focus on the expected investment risk.tolerance for risk rather than focus on the expected investment risk.

ReferencesReferencesReferencesReferences1.1. Schaum's Outline of Theory and Problems of Financial Schaum's Outline of Theory and Problems of Financial

M t d diti 1998 JAE K SHIM Ph DM t d diti 1998 JAE K SHIM Ph DManagement, second edition, 1998; JAE K. SHIM, Ph.D Management, second edition, 1998; JAE K. SHIM, Ph.D and JOEL. G. SIEGEL, Ph.D.CPAand JOEL. G. SIEGEL, Ph.D.CPA

2.2. Fundamentals of Corporate Finance Third Edition, Fundamentals of Corporate Finance Third Edition, 20012001 Ri h d A B l St t C M Al JRi h d A B l St t C M Al J2001;2001; Richard A. Brealey, Stewart C. Myers, Alan J. Richard A. Brealey, Stewart C. Myers, Alan J. Marcus, and Wallace E. CarrollMarcus, and Wallace E. Carroll

3.3. Slides handouts from internet search_google_Cash Slides handouts from internet search_google_Cash flow analysis pptflow analysis pptflow analysis.ppt.flow analysis.ppt.

4.4. http://www.coba.usf.edu/departments/finance/faculty/http://www.coba.usf.edu/departments/finance/faculty/besley/notes/risk.pdfbesley/notes/risk.pdfhtt // b d / d l /f434/t t / ldhtt // b d / d l /f434/t t / ld5.5. http://www.cbpa.ewu.edu/~deagle/f434/termstruc/sldhttp://www.cbpa.ewu.edu/~deagle/f434/termstruc/sld003.htm003.htm

6.6. http://www.finance.google.com/http://www.finance.google.com/

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risk and rate of return

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