Copyright © 2011 Pearson Prentice Hall. All rights reserved. Chapter 4 Return and Risk.

Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Chapter 4

Return and Risk

Copyright © 2011 Pearson Prentice Hall. All rights reserved.4-2

The Concept of Return

• Return– The level of profit from an investment, or– The reward for investing

• Components of Return– Income: cash or near-cash that is received as a result of owning

an investment– Capital gains (or losses): the difference between the proceeds

from the sale of an investment and its original purchase price

• Total Return: the sum of the income and the capital gain (or loss) earned on an investment over a specified period of time


Why Return is Important

• Allows comparison of actual or expected gains with the levels of gain needed

• Allows us to “keep score” on how our investments are doing compared to our expectations

• Historical Performance– Provides a basis for future expectations– Does not guarantee future performance

• Expected Return– Return an investor thinks an investment will earn in the future– Determines what an investor is willing to pay for an investment or

if they are willing to make an investment


Key Factors in Return

• Internal Characteristics– Type or risk of investment– Issuer’s management– Issuer’s financing

• External Forces– Political environment– Business environment– Economic environment– Inflation– Deflation


Table 4.4 Historical Returns for Popular Security Investments (1926-2005)

1/1/1979 to 8/11/2011 (32.5 years)

S&P500 Composite Total Return 11.13%

Russel 3000 Index 12.42%

Wilshire 5000 11.19%


The Time Value of Money and Returns

• The sooner you receive a return on a given investment, the better

• A dollar received today is worth more than a dollar received in the future

• The sooner your money can begin earning interest, the faster it will grow


Determining a Satisfactory Investment

• Satisfactory Investment: one for which the present value of benefits equals or exceeds the present value of its costs

• If Value >= Market Value, BUY• If IRR >= Required Return, BUY


Measuring Return

• Required Return– The rate of return an investor must earn on an

investment to be fully compensated for its risk

Required returnon investment j

Real rateof return

Expected inflation

premium

Risk premiumfor investment j

Required returnon investment j

Risk-free

rate

Risk premiumfor investment j


Measuring Return (cont’d)• Real Rate of Return

– Equals the nominal rate of return minus the inflation rate– Measures the change in purchasing power provided by an

investment

• Expected Inflation Premium– The average rate of inflation expected in the future

• Risk-free Rate– The rate of return that can be earned on a

risk-free investment– The most common “risk-free” investment is considered to be the

3-month U.S. Treasury Bill

Risk-free rate Real rateof return

Expected inflation

premium

RF r* IP


Measuring Return (cont’d)• Risk Premium

– Additional return an investor requires on a risky investment to compensate for risks based upon issue and issuer characteristics

– Issue characteristics are the type, maturity and features

– Issuer characteristics are industry and company factors

• Required Return– The rate of return an investor must earn on an

investment to be fully compensated for its risk

premium riskRF

premium risk inflation expected rate realreturn quiredRe


Holding Period Return (HPR)

• Holding Period: the period of time over which an investor wishes to measure the return on an investment vehicle

• Realized Return: current return actually received by an investor during the given return period

• Paper Return: return that has been achieved but not yet realized (no sale has taken place)


Table 4.6 Key Financial Variables for Four Investment Vehicles

Beginning Value $2,000.00

Ending Value $2,200.00

Investment Cash Flows $45.00

Investment Time (Yrs) 1.000

HPR (annualized return) 12.250%

Holding Period Return


Future values

– N = years– I/Y = annual interest – PV = current value (-CF)

• invest 1000 at 10% for 4 years

)FVIF(*PV)k1(*PVFV k,nn =+=

time value of money

Future Value (FV) Solve for PV

Present Value (PV) -$1,000.00

Annual Interest Rate (I/Y) 10.00% Solve for FV $1,464.10

Time in Years (N) 4.00

Solve for Interest Rate

Compounding Freq. (m) (P/Y) 1


Compounding more frequently

• Compounding periods = P/Y = m =periods per years • Invest 1000 for 6 years at 12% compounded semi-annually

time value of money



Annual Interest Rate (I/Y) 12.00% Solve for FV $2,012.20




Solve for Time

Is this an Ordinary Annuity (y/n) y

Payment (PMT) (A) Effective Interest Rate 12.36%


Nominal and effective rates

• Nominal - stated or contractual int rate, annual interest rate (I/Y)

• Effective – EAR -true rate (APR)

i = 12% m = 1 ieff = 12.00%m = 2 i = 12.36m = 4 i = 12.55m = 12 i = 12.68

0.1//

1/

YP

YPYI

EAR


Present value (Discounting)

What is the present value of $1000 3 years from now if can invest at 13%

PVIF*FV)m/k1

1(*FVPV m

time value of money

Future Value (FV) $1,000.00 Solve for PV -$693.05

Present Value (PV)

Annual Interest Rate (I/Y) 13.00% Solve for FV





Annuities

• Equal cash flow for a certain period of time

– ordinary CF starts at end of yr– annuity due starts with CF today


Future Value of an Annuity

What if you made monthly payments ($416.67)?

4,901,988

time value of money

» FVA = pmt * (FVIFA)

Start at age 20 invest $5000 per year in an IRA until age 60 @ 12% FVA = 5000( 767.080) = 3,835,457

Annual Interest Rate (I/Y) 12.00% Solve for FV $0.00




Solve for Time


Payment (PMT) (A) -$5,000.00 Effective Interest Rate 12.00%

Growth of an Annuity

Growth of a Perpetuity PVA

PMT for PVA

Interest for PVA #NUM!

FVA $3,835,457.10


You have determined that you will need 1,250,000 in 30 years to retire and can earn 10%. What is the monthly payment to get the future amount ?

time value of money

Future Value (FV) $1,250,000.00 Solve for PV -$63,012.29

Present Value (PV)

Annual Interest Rate (I/Y) 10.00% Solve for FV




Solve for Time





PMT for PVA -$552.98


FVA

PMT for FVA -$552.98


• You have now accumulated that $1,250,000 in an investment account. You want to withdraw an equal amount each year for 20 years and can invest at 10%. How much can you withdraw annually? Monthly?

Monthly $12,062time value of money


Present Value (PV) $1,250,000.00

Annual Interest Rate (I/Y) 10.00% Solve for FV -$8,409,374.94




Solve for Time





PMT for PVA -$146,824.53

Interest for PVA -99.911%

FVA

PMT for FVA -$146,824.53


n

n

growth/wr1

g11*

gr

1APIF

time value of money

Growing annuity

• You would like to retire with a 100,000 per year income. If you were to live for 35 years in retirement and could earn 8%. How much would you need to acquire in your retirement accounts?

• You are concerned about inflation. If you desired for your income to keep pace with a 4% inflation rate, how much would you need?





Solve for Time


Payment (PMT) (A) $100,000.00 Effective Interest Rate 8.00%

Growth of an Annuity 4.00%

Growth of a Perpetuity PVA -$1,165,456.82

PMT for PVA


FVA

PMT for FVA

Interest for FVA

PV of Perpetuity $1,250,000.00

PV of Growing Annuity -$1,832,770.19


PerpetuitiesPVperp = Pmt / IIf you wanted to start an annual endowment that would provide your favorite professor

(ME) with 20,000 per year, and the college could earn 10% per year, how much would you have to donate? PV = 20,000 / .10 = 200,000

• What if you wanted the payment to grow with inflation of 4%

time value of money


Time in Years (N)



Solve for Time #DIV/0!


Payment (PMT) (A) $25,000.00 Effective Interest Rate 10.00%


Growth of a Perpetuity 4.00% PVA $0.00

PMT for PVA


FVA

PMT for FVA

Interest for FVA

PV of Perpetuity $250,000.00

PV of Growing Annuity

PV of Growing Perpetuity -$433,333.33


Example

• You currently earn 50,000 per year and have been able to save $15,000 in a retirement account. You will retire in 35 years at age 60 and inflation is 4%. What will your income need to be in year 1 of retirement to maintain your current lifestyle?

• If you live to 90, how much do you need in your pension fund at age 60 with 8% return.

• If you wanted your retirement income to keep up with an expected inflation rate of 4.5%, how much would you need?

• How much must you invest each month in your retirement plans to get your desired growing retirement income if you can earn a 12% return?

$197,304

$2,221,205

Monthly 397.99

$3,539,071

PV = 50K FV = ? N=35 I/Y=4% m=1 PMT = 0

PVA = ? FV = 0 N=30 I/Y=8% m=1 PMT = 197304

PVA = ? FV = 0 N=30 I/Y=8% m=1 PMT = 197304

Growth of annuity = 4.5%

PV = -15000 FV = 3539071 N=35 I/Y=12% m=12

PMT for FVA = ?


You currently have $5,000 in your 401k. You are 35 years old and plan to retire in 25 years. You also have estimated that you will need 2 million dollars in your retirement account. You are currently investing $250 per month and your company matches that amount. What rate of return must your retirement account earn to meet your goal?

time value of money

Future Value (FV) $2,000,000.00 Solve for PV


Annual Interest Rate (I/Y) Solve for FV


Solve for Interest Rate 18.56%


Solve for Time


Payment (PMT) (A) -$500.00 Effective Interest Rate 20.23%



PMT for PVA

Interest for PVA 1.167%

FVA $170,000.00

PMT for FVA

Interest for FVA 14.01%

PV of Perpetuity #DIV/0!

PV of Growing Annuity

PV of Growing Perpetuity #DIV/0!


Using IRR in Investment Decisions

• Internal Rate of Return: determines the compound annual rate of return earned on an investment held for longer than one year

• Advantages of Internal Rate of Return– Uses the time value of money– Allows investments of different investment periods to be

compared with each other– If the yield is equal to or greater than the required return,

the investment is acceptable

• Disadvantages of Internal Rate of Return– Calculation is complex


Solve for Returns

• Bought an asset 5 yrs ago for $50, now worth $75. What return?

time value of money

Future Value (FV) $75.00 Solve for PV

Present Value (PV) -$50.00

Annual Interest Rate (I/Y) Solve for FV


Solve for Interest Rate 8.45%



Yield (IRR) for a Stream of Income

• Some investments, such as bonds, provide uneven streams of income over the investment period

• Calculate yield (IRR) by finding the discount rate that equates the PV of the investment’s income stream to its market price

Pds Cash Flow0 -$1,1001 $90 Discount Rate 14.00%2 $1003 $110 Number of Periods 74 $1205 $100 PV of Future Cash Flows $878.256 $1007 $1,200 Net Present Value -$22289 IRR 9.32%

TV Mixed Cash Flows


Interest on Interest: The Critical Assumption

• Using yield (IRR) to measure return assumes that all income earned over the investment horizon is reinvested at the same rate as the original investment.

• Reinvestment Rate is the rate of return earned on interest or other income received from an investment over its investment horizon.

• Fully compounded rate of return is the rate of return that includes interest earned on interest.


Sources of Risk

• Risk-Return Tradeoff is the relationship between risk and return, in which investments with more risk should provide higher returns, and vice versa

• Risk is the chance that the actual return from an investment may differ from what is expected


Sources of Risk (cont’d)

• Currency Exchange Risk is the risk caused by the varying exchange rates between the currencies of two countries. (Discussed in Chapter 2)

• Types of Investments Affected– International stocks or ADRs– International bonds

• Examples of Currency Exchange Risk– U.S. dollar gets “stronger” against foreign currency,

reducing value of foreign investment



• Business Risk is the degree of uncertainty associated with an investment’s earnings and the investment’s ability to pay the returns owed to investors.

• Types of Investments Affected– Common stocks – Preferred stocks

• Examples of Business Risk– Decline in company profits or market share– Bad management decisions



• Financial Risk is the degree of uncertainty of payment resulting from a firm’s mix of debt and equity; the larger the proportion of debt financing, the greater this risk.

• Types of Investments Affected– Common stocks– Corporate bonds

• Examples of Financial Risk– Company can’t get additional loans for growth or to fund

operations– Company defaults on bonds



• Purchasing Power Risk is the chance that changing price levels (inflation or deflation) will adversely affect investment returns.

• Types of Investments Affected– Bonds (fixed income)– Certificates of deposit

• Examples of Purchasing Power Risk– Movie that was $8.00 last year is $9.00 this year



• Interest Rate Risk is the chance that changes in interest rates will adversely affect a security’s value.

• Types of Investments Affected– Bonds (fixed income)– Preferred stocks

• Examples of Interest Rate Risk– Market values of existing bonds decrease as market interest rates

increase– Income from an investment is reinvested at a lower interest rate

than the original rate



• Liquidity Risk is the risk of not being able to liquidate an investment conveniently and at a reasonable price.

• Types of Investments Affected– Some small company stocks– Real estate

• Examples of Liquidity Risk– The price of a house has to be lowered for a quick sale



• Tax Risk is the chance that Congress will make unfavorable changes in tax laws, driving down the after-tax returns and market values of certain investments.

• Types of Investments Affected– Municipal bonds– Real estate

• Examples of Tax Risk– Lower tax rates reduce the tax benefit of municipal bond interest– Limits on deductions from real estate losses



• Market Risk is the risk of decline in investment returns because of market factors independent of the given investment.

• Types of Investments Affected– All types of investments

• Examples of Market Risk– Stock market decline on bad news– Political upheaval– Changes in economic conditions



• Event Risk comes from an unexpected event that has a significant and unusually immediate effect on the underlying value of an investment.

• Types of Investments Affected– All types of investments

• Examples of Event Risk– Decrease in value of insurance company stock after

a major hurricane– Decrease in value of real estate after a major earthquake


Measures of Risk: Single Asset

• Standard deviation is a statistic used to measure the dispersion (variation) of returns around an asset’s average or expected return

• Coefficient of variation is a statistic used to measure the relative dispersion of an asset’s returns; it is useful in comparing the risk of assets with differing average or expected returns

• Higher values for both indicate higher risk

Copyright © 2011 Pearson Prentice Hall. All rights reserved.4-40 4-40

Risk Measurement

• The expected value of a return, k-bar, is the most likely return of

an asset (average, mean).

• The most common statistical indicator of an asset’s risk is the

standard deviation, σk, which measures the dispersion around the

expected value.

• Coefficient of variation

– For making risk comparisons

)k(EPr*kk jj ∑

∑ - j

2

j Pr*kk

∧

kCV


stand alone risk

Economic Conditions Probability Asset A Asset B Asset C

Very Good

Good 0.250 20.00% -2.00% 4.00%

Average 0.500 10.00% 5.00% 4.00%

Bad 0.250 -5.00% 7.00% 4.00%

Very Bad

Total Probabilities 1.000

Portfolio Weights 0.70 0.30 0.00

Statistics Asset A Asset B Asset C Portfolio

Expected Return 8.750% 3.750% 4.000% 7.250%

Variance 0.797% 0.117% 0.000% 0.289%

Standard Deviation 8.927% 3.419% 0.000% 5.380%

Coefficient of Var 1.020 0.912 - 0.742

scroll right for Efficent Frontier


Table 4.10 Historical Returns and Standard Deviations for Select Asset Classes (1900–2008)


Figure 4.2 Risk-Return Tradeoffs for Various Investment Vehicles


Acceptable Levels of Risk Depend Upon the Individual Investor

• Risk-indifferent describes an investor who does not require a change in return as compensation for greater risk

• Risk-averse describes an investor who requires greater return in exchange for greater risk

• Risk-seeking describes an investor who will accept a lower return in exchange for greater risk


Real data risk and return• Uses sample statistics• Start with monthly prices of a set of assets

• Calculate the monthly returns and the statistics of those assets

BUA350 Project 1 Data

BUA350 Project 2


Historical Data Returns

data pts Return Asset A Returns Asset B1 19.10% 8.10%2 -0.70% 10.20%3 10.40% 13.50%4 24.80% 13.80%5 7.40% 15.40%

Mean 12.200% 12.200%Stnd Deviation 9.988% 2.971%Coef. of Var 0.8187 0.2435 data points 5 5


Steps in the Decision Process:Combining Return and Risk

• Estimate the expected return using present value methods and historical/projected return rates

• Assess the risk of the investment by looking at historical/projected returns using standard deviation or coefficient of variation of returns

• Evaluate the risk-return of each investment alternative to make sure the return is reasonable given the level of risk

• Select the investment vehicles that offer the highest expected returns associated with the level of risk you are willing to accept

Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Chapter 4

Additional Chapter Art


Table 4.1 Profiles of Two Investments


Table 4.2 Total Returns of Two Investments


Table 4.3 Historical Investment Data for ExxonMobil Corp. (XOM)


Table 4.8 Historical Returns for ExxonMobil and Panera Bread


Table 4.9 Calculation of Standard Deviations of Returns for ExxonMobil and Panera Bread


Investment Profile

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Copyright © 2011 Pearson Prentice Hall. All rights reserved. Chapter 4 Return and Risk.

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