Berlin, 04.01.2006Fußzeile1 The Trade-off Between Risk and Return Professor Dr. Rainer Stachuletz...

Berlin, 04.01.2006 Fußzeile 1

The Trade-off Between

Risk and Return

Professor Dr. Rainer Stachuletz

International Markets and Corporate Finance

Berlin School of Economics and Law


Risk and Return

The return earned on investments represents the marginal benefit of investing.

Risk represents the marginal cost of investing.

A trade-off always arises between expected risk and expected return.


Risk and Return

Valuing risky assets - a task fundamental to financial management

Three-step procedure for valuing a risky asset

1. Determine the asset’s expected cash flows2. Choose discount rate that reflects asset’s risk3. Calculate present value (PV cash inflows - PV

outflows)The three-step procedure is called

discounted cash flow (DCF) analysis.


Financial Return

Total return: the total gain or loss experienced on an investment over a given

period of time

Component

s of the total return

Income stream from the investment

Capital gain or loss due to changes in asset prices

Total return can be expressed either in dollar terms or in percentage terms.


Dollar Returns

Total dollar return = income + capital gain / loss

Terrell bought 100 shares of Micro-Orb stock for $25

A year later:Dividend = $1/shareSold for $30/share

Dollar return = (100 shares) x ($1 + $5) = $600

Owen bought 50 shares of Garcia Inc. stock for $15

A year later:No dividends paidSold for $25/share

Dollar return = (50 shares) x ($10)

= $500


Percentage Returns

Terrell’s dollar return exceeded Owen’s by $100. Can we say that Terrell was better off?

No, because Terrell and Owen’s initial investments were different: Terrell spent $2,500 in initial

investment, while Owen spent $750.

Percentage return: total dollar return divided by the initial investment

investment initial

return dollar totalreturn percentage Total


Percentage Returns

%2424.0

500,2$

5$1$100 '

returnpercentagesTerrell

%6767.0

750$

10$50 '

returnpercentagesOwen

In percentage terms, Owen’s investment performed better than Terrell’s


$1 Investment in Equities, Treasury Bonds and Bills

Year

$15,579

$148

$61

$22

10,000

100,000

1,000

100

10

1

Equities Bonds

Bills Inflation

1900 1920 1940 1960 1980 2000 2003


Percentage Returns on BillsBonds, and Stocks

Difference between average return of stocks and bills = 7.6%

Difference between average return of stocks and bonds = 6.5%

Risk premium: the difference in returns offered by a risky asset relative to the risk-free return

available

Nominal (%) Real (%)Asset Class Average Best Year Worst Year Average Best Year Worst Year

Bills 4.1 14.7 0.0 1.1 19.7 -15.1Bonds 5.2 40.4 -9.2 2.3 35.1 -19.4Stocks 11.7 57.6 -43.9 8.5 56.8 -38


Distribution of Historical Stock Returns, 1900 - 2003

Histogram of Nominal Returns on Equities 1900-2003

<-30 -30 to -20 to -10 to 0 to 10 to 20 to 30 to 40 to >50 -20 -10 0 10 20 30 40 50

Percent return in a given year

Probability distribution for future stock returns is unknown. We can approximate the unknown distribution by assuming a normal

distribution.


Variability of Stock Returns

Normal distribution can be described by its mean and its variance.

Variance (2) - the expected value of squared deviations from the mean

1

)(1

2

2

N

RRVariance

N

tt

Variance (%-squared) - hard to interpret, so calculate standard deviation, a measure of volatility equal to

square root of 2


Volatility of Asset Returns

Asset Average(%) Std. Dev. (%) Average(%) Std. Dev. (%)

Equities 11.7 20.1 8.5 20.4Bonds 5.2 8.2 2.3 10Bills 4.1 2.8 1.1 4.7

Nominal Returns Real Returns

Asset classes with greater volatility pay higher average returns.

Average return on stocks is more than double the average return on bonds, but stocks are 2.5 times more volatile.


Average Returns and St. Dev. for Asset Classes

1. Investors who want higher returns have to take more risk2. The incremental reward from accepting more risk seems

constant

Bills Bonds

Stocks

Average Return (%)

Standard Deviation (%)


Average Return / Standard Dev.Individual Securities, 1994-2003

For various asset classes, a trade-off arises between risk and return. Does the trade-off appear to hold for all individual

securities?

Company Average Return(%) Std Deviation(%)

Anheuser-Busch 19.2 16.1Coca Cola 12.1 22.6Wendy's International 11.8 23.3Archer Daniels Midland 7.6 23.5General Motors 8.3 26.0General Electric 20.3 32.1Merck 17.8 32.7Nordstrom 14.3 38.1Wal-Mart 22.7 44.7American Airlines (AMR) 10.0 47.8Advanced Micro Devices (AMD) 17.6 56.4Average for all 11 stocks 14.7 33.0Average for U.S stocks 12.5 21.0


Average Return (%)

Standard Deviation (%)

Wal-MartAnheuser-Busch

Archer Daniels Midland

American Airlines

No obvious pattern here !!!

Average Return / Standard Dev.Individual Securities, 1994-2003


Diversification

Most individual stock prices show higher volatility than the price volatility of portfolio of all common stocks.

How can the standard deviation for individual stocks be higher than the standard deviation of the portfolio?

Diversification: investing in many different assets reduces the volatility of the portfolio.

The ups and downs of individual stocks partially cancel each other out.


Number of StocksNumber of Stocks

Systematic RiskSystematic Risk

1 2 3 111 2 3 11

Portfolio of 11 stocks

AMD

Unsystematic RiskUnsystematic Risk

AMD + American Airlines

AMD + American Airlines + Wal-Mart

The Impact of Additional Assets on the Risk of a Portfolio

Po

rtfo

lio

Sta

nd

ard

Dev

iati

on


Diversification reduces portfolio volatility, but only up to a point. Portfolio of all stocks still has a volatility of 21%.

Systematic risk: the volatility of the portfolio that cannot be eliminated through diversification.

Unsystematic risk: the proportion of risk of individual assets that can be eliminated through diversification

What really matters is systematic risk….how a group of assets move together.

Systematic and Unsystematic Risk


Anheuser Busch stock had higher average returns than Archer-Daniels-Midland stock, with

smaller volatility.

Systematic and Unsystematic Risk

American Airlines had much smaller average returns than Wal-Mart, with similar volatility.

The tradeoff between standard deviation and average returns that holds for asset classes

does not hold for individual stocks.

Because investors can eliminate unsystematic risk through diversification, market rewards only

systematic risk.

Standard deviation contains both systematic and unsystematic risk.


• Investment performance is measured by total return.

• Trade-off between risk and return for assets: historically, stocks had higher returns and volatility than bonds and bills.

• One measure of risk: standard deviation (volatility)

• Unsystematic and systematic risk: risk that can (cannot) be eliminated through diversification, respectively

Risk and Return

Berlin, 04.01.2006Fußzeile1 The Trade-off Between Risk and Return Professor Dr. Rainer Stachuletz...

Documents

Transcript of Berlin, 04.01.2006Fußzeile1 The Trade-off Between Risk and Return Professor Dr. Rainer Stachuletz...