Slides CH06

The Meaning and Measurement of Risk and Return

Chapter 6

Keown, Martin, Petty - Chapter 6 2

Learning Objectives

1. Define and measure the expected rate of return of an individual investment.

2. Define and measure the riskiness of an individual investment.

3. Compare the historical relationship between risk and rates of return in the capital markets.

4. Explain how diversifying investments affects the riskiness and expected rate of return of a portfolio or combination of assets.

5. Explain the relationship between an investor’s required rate of return on an investment and the riskiness of the investment.


Slide Contents

1. Principles Used in this chapter2. Expected return3. Risk4. Portfolio and Diversification5. Required rate of return and CAPM


Expected Cash Flows and Expected Return The expected benefits or returns,

an investment generates come in the form of cash flows.

Cash flows are used to measure returns (not accounting profits).


The expected cash flow is the weighted average of the possible cash flow outcomes such that the weights are the probabilities of the occurrence of the various states of the economy.

Expected Cash flow (X) = ΣPi*xi Where Pi = probabilities of outcome i

xi = cash flows in outcome i

Expected Cash Flows and Expected Return


Measuring the Expected Cash Flow and Expected Return

State of the economy

Probability of the states

Cash flow from the investment

% Return (Cash Flow/Inv. Cost)

Economic Recession

20% $1,000 10% ($1,000/$10,000)

Moderate Economic Growth

30% 1,200 12% ($1,200/$10,000)

Strong Economic Growth

50% 1,400 14% ($1,400/$10,000)


Expected Cash Flow

Expected Cash flow = Σ Pi*xi

= .2*1000 + .3*1200 + .5*1400

= $1,260 on $1,000 investment


Expected Rate of Return We can also determine the % of expected

return on $1,000 investment. Expected Return is the weighted average of all the possible returns, weighted by the probability that each return will occur.

Expected Return (%) = Σ Pi*ki Where Pi = probabilities of outcome i

ki = expected % return in outcome i


Expected Return (%) = Σ Pi*ki Where Pi = probabilities of outcome i

ki = expected % return in outcome i

= .2(10%) + .3 (12%) + .5(14%)= 12.6%

Expected Rate of Return


Risk

Three important questions:

1. What is risk?

2. How do we measure risk?

3. Will diversification reduce the risk of portfolio?


Risk – Defined

Risk refers to potential variability in future cash flows.

The wider the range of possible future events that can occur, the greater the risk.

Thus, the returns on common stock is more risky than returns from investing in a savings account in a bank.


Risk – Measurement

Standard deviation (S.D.) is one way of measuring risk. It measures the volatility or riskiness of portfolio returns.

S.D. = square root of the weighted average squared deviation of each possible return from the expected return.


Example

Two Investment Options:

1. Invest in a Treasury bill that offers a 6% annual return.

2. Invest in stock of a local publishing company with an expected return of 15% based on the payoffs (given on next slide).


Probability of Payoffs Probability Rate of Return Treasury Bill 100% 6% Stock 10% 0% 20% 5% 40% 15% 20% 25% 10% 30%


Stock of publishing company is more risky but it also offers the potential of a higher payoff.


Risk & Return: Historical Perspective (1990-2005)


Portfolio Portfolio refers to combining several

assets.

Examples of portfolio:

Investing in multiple financial assets (stocks – $6000, bonds – $3000, T-bills – $1000)

Investing in multiple items from single market (example – invest in 30 different stocks)


Reducing Total Risk or Variability in a Portfolio

Total risk of Portfolio is due to two types of Risk:

Systematic (or Market risk) that affects all firms (ex. Tax rate changes, war)

Non-systematic (or company unique) risk that affects only a specific firm (ex. Labor strikes, CEO change)

Only non-systematic risk can be reduced or eliminated through effective diversification (figure 6-3)


Total Risk & Unsystematic Risk Decline as Securities Are Added.


The main motive for holding multiple assets or creating a portfolio of stocks (called diversification) is to reduce the overall risk exposure. The degree of reduction depends on the correlation among the assets.

If two stocks are perfectly positively correlated, diversification has no effect on risk.

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

Thus while building a portfolio, we should pick securities/assets that have negative or low positive correlation to attain diversification benefits.


The relationship between B&N and S&P500 is captured well in figure 6-5.

Characteristic line is the “line of best fit” for all the stock returns relative to returns of S&P500.

The slope of the characteristic line (=1.40) measures the average relationship between a stock’s returns and those of the S&P 500 Index Returns. This slope (called beta) is a measure of the firm’s market risk.

Measuring Market Risk: Barnes and Noble versus S&P500


Interpreting Beta Beta is the risk that remains for a company

even after diversifying the portfolio. A stock with a Beta of 0 has no systematic risk A stock with a Beta of 1 has systematic risk equal

to the “typical” stock in the marketplace A stock with a Beta exceeding 1 has systematic

risk greater than the “typical” stock

Most stocks have betas between .60 and 1.60. Note, the value of beta is highly dependent on the methodology and data used.


Portfolio Beta

Portfolio beta indicates the percentage change on average of the portfolio for every 1 percent change in the general market.

ßportfolio= Σ wj*ßj

Where wj = % invested in stock jßj = Beta of stock j


Portfolio BetaHolding-Period Returns: High- and Low-Beta Portfolios and the

S&P 500 Index


Asset Allocation

Asset allocation refers to diversifying among different kinds of asset types (such as treasury bills, corporate bonds, common stocks).

An asset allocation decision has to be made today – the payoff in the future will depend on the mix chosen before, which cannot be changed. Hence asset allocation decisions are considered the “most important decision” while managing an investment portfolio.


In 2002, $1,000 invested in stock market will have earned less than $1,000 invested in banks

In 2003, $1,000 in stocks will have earned higher returns

History shows asset allocation matters and that taking high risk does not always pay off!!!

Of course, the decision has to be made today for the future and that is why asset allocation decisions determine who will be the “winners” in the financial market!!!

Example


Asset Allocation Example Determine the final value of the portfolio based

on the following two portfolios with a 75-year time horizon. Use the average returns from the previous slide and $1m initial investment.

Conservative investor– invests 20% in Tbills, 40% in Govt. bonds and 40% in Corporate Bonds

Aggressive investor – invests 10% in Tbills, 50% in small company stocks and 40% in common stocks


Asset Allocation Matters!

Return = Σ Weightj*Return%j

Conservative investor = 5.42% Aggressive investor = 14.24%

Final Value = $1m(1+i)75

Conservative =$52,387,284.93 Aggressive = $21,695,246,174.70



Required Rate of Return

Investor’s required rate of returns is the minimum rate of return necessary to attract an investor to purchase or hold a security.

This definition considers the opportunity cost of funds, i.e. the foregone return on the next best investment.


Required Rate of Return

k=kfr + krp

Where:

k = required rate of returnkfr = risk-Free Rate

krp = risk Premium


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 risk increases, we will demand additional expected returns.


k=kfr + krp

Or

Risk Premium = Required Return – Risk-Free rate

krp = k - kfr

Measuring the Required Rate of Return


Capital Asset Pricing Model

CAPM equates the expected rate of return on a stock to the risk-free rate plus a risk premium for the systematic risk.

CAPM provides for an intuitive approach for thinking about the return that an investor should require on an investment, given the asset’s systematic or market risk.


If the required rate of return for the market portfolio km is 12%, and the krf is 5%, the risk premium krp for the market would be 7%.

This 7% risk premium would apply to any security having systematic (nondiversifiable) risk equivalent to the general market, or beta of 1.

In the same market, a security with Beta of 2 would provide a risk premium of 14%.

Capital Asset Pricing Model


CAPM

CAPM suggests that Beta is a factor in required returns.

kj = krf + B(market rate – risk-free rate)


CAPM

Example:Market risk = 12%Risk-free rate = 5%5% + B(12% - 5%)If B = 0, Required rate = 5%If B = 1, Required rate = 12%If B = 2, Required rate = 19%


The Security Market Line (SML)

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.


The Security Market Line

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