Investment Risk

Eric HigginsDepartment of Finance, KSU

Investing

• Investing– Definition of an investment: The current

commitment of dollars for a period of time in order to get future payments• Put in money today to get more in the future

Investing

• Risk -- Risk is the possibility that you won’t get back what you expect– The problem with ignoring risk: • Things sound too good• Don’t consider the downside

Investment

• What are some investment options?– Bank Account– Bonds– Stocks– Real Estate– Art– Private Investment

How Risky are Investments

• Rank the following investments in terms of risk …– An FDIC insured bank account– An investment in the debt of Microsoft– A 10-year government bond– A friend wants you to invest in his idea to open a

new barbershop– A share of IBM stock– Buying a house

How Risky are Investments• Risk ranking…– An FDIC insured bank account– A 10-year government bond– An investment in the debt of Microsoft– Buying a house– A share of IBM stock– A friend wants you to invest in his idea to open a new

barbershop• http://www.finrafoundation.org/resources/education/mo

dules/

• http://www.callan.com/research/periodic/

Investing

• Lesson:– Higher risk, higher return– Put money in a bank savings account, get 2%

return guaranteed– Put money in the stock market, get 11% with the

chance that you may lose money

Compound Interest

• The principle of compounding means that you earn interest on interest

• Three things to consider– Invest early– Invest often– Have patience

Risk

• How risky are you?• You have the following choice for your salary

in the first year that you graduate:– $50,000 for certain– A coin-flip where you get either $100,000 or $0

Probability

• What is more likely?– Two people in this room have the same birthday– Somebody in this room has a birthday on October

31• Two people having the same birthday is actually much

more likely

• You have to understand the role of probability in making investment decisions– Relates to risk

Expected Returns

• Expected returns are based on the probabilities of possible outcomes

• In this context, “expected” means average if the process is repeated many times

• The “expected” return does not even have to be a possible return

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Required Returns and Risk

• Suppose we have two assets, A and B, that are both expected to return 15% and have a price of $100. (thus, both stocks will return $15)

• Suppose that stock A is riskier than stock B.• What would happen?• What if the price of A fell to $75 and B rose to

$150?

Required vs. Expected Returns

• Expected returns are what an investment will earn

• Required returns are what an investment should earn

• The two may differ, creating investment opportunities

Example: Expected Returns• Suppose you have predicted the following returns for

stocks C and T in three possible states of nature. What are the expected returns?– State Probability C T– Boom 0.3 0.15 0.25– Normal 0.5 0.10

0.20– Recession ??? 0.02 0.01

• RC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.99%• RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%

Variance and Standard Deviation

• Variance and standard deviation still measure the volatility of returns

• Using unequal probabilities for the entire range of possibilities

• Weighted average of squared deviations

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Example: Variance and Standard Deviation

• Consider the previous example. What are the variance and standard deviation for each stock?

• Stock C– 2 = .3(.15-.099)2 + .5(.1-.099)2 + .2(.02-.099)2

= .002029– = .045

• Stock T– 2 = .3(.25-.177)2 + .5(.2-.177)2 + .2(.01-.177)2

= .007441– = .0863

Another Example• Consider the following information:– State Probability ABC, Inc.– Boom .25 .15– Normal .50 .08– Slowdown .15 .04– Recession .10 -.03

• What is the expected return?• What is the variance?• What is the standard deviation?

Portfolios

• A portfolio is a collection of assets• An asset’s risk and return is important in how

it affects the risk and return of the portfolio• The risk-return trade-off for a portfolio is

measured by the portfolio expected return and standard deviation, just as with individual assets

Example: Portfolio Weights

• Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security?– $2000 of DCLK– $3000 of KO– $4000 of INTC– $6000 of KEI

•DCLK: 2/15 = .133•KO: 3/15 = .2•INTC: 4/15 = .267•KEI: 6/15 = .4

Portfolio Expected Returns• The expected return of a portfolio is the weighted average of

the expected returns for each asset in the portfolio

• You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities

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Example: Expected Portfolio Returns

• Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?– DCLK: 19.65%– KO: 8.96%– INTC: 9.67%– KEI: 8.13%

• E(RP) = .133(19.65) + .2(8.96) + .167(9.67) + .4(8.13) = 9.27%

Perfect Negative Correlation

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Perfect Positive Correlation

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The Principle of Diversification• Diversification can substantially reduce the variability

of returns without an equivalent reduction in expected returns

• This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another

• However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

Figure 13.1

Savings Game

• Start with $1,000– You need to pick a risk category– High risk earns 2X the market return, Medium risk earns

the market return, Low risk earns ½ the market return.– Market returns will be determined randomly.– Each “round” represents 5 years. We will play four

rounds.– You can change your risk category after every round– Goal is to end up with the most money at the end of the

game.

Savings Game

• In addition to ending up with the most money you have to have:– $500 at the end of round 2 to put a down

payment on a car– If you don’t meet the goal, you lose $1,000 on

your ending total.

Round 1

• We will randomly choose a card from a deck of cards.– Red means loss, black means gain– Amount of gain/loss equal to the amount on the

card, face cards all 10% gain/loss

Round 2

• If the market went up in Round 1, it is likely that the market will go down in Round 2.

• If the market went down in Round 1, it is likely that the market will go up in Round 2.

• I will now remove one suit (red or black) from the deck of cards and we will draw again.

• Remember– You need $500 at the end of Round 2– The probability of the market going up/down has changed.

It is not random any more.

Round 3

• Risk aversion…choice of certain vs. uncertain payoff– You can either go up 5%• Risk doesn’t matter here. If you choose this you get

5%.– I will flip a coin, heads the market goes up 10%

tails the market goes down 5%. • Risk matters if you take the gamble. High risk gets 2X

market, medium risk gets market, low risk gets ½ market

Round 4

• Roll the Dice– I will roll two dice…• 5, 6, 7, 8, 9 the market goes up 10%• 2, 3, 4, 10, 11, 12 the market goes down 5%

– Think about the odds, what is most likely to happen?

– Choose your risk level carefully this is the last round

Rounds 1, 2:Card DrawRed Low Medium High Black Low Medium High

2 0.95 0.90 0.82 2 1.05 1.10 1.223 0.93 0.86 0.73 3 1.08 1.16 1.344 0.90 0.82 0.66 4 1.10 1.22 1.475 0.88 0.77 0.59 5 1.13 1.28 1.616 0.86 0.73 0.53 6 1.16 1.34 1.767 0.84 0.70 0.47 7 1.19 1.40 1.938 0.82 0.66 0.42 8 1.22 1.47 2.109 0.79 0.62 0.37 9 1.25 1.54 2.29

10 0.77 0.59 0.33 10 1.28 1.61 2.49J 0.77 0.59 0.33 J 1.28 1.61 2.49Q 0.77 0.59 0.33 Q 1.28 1.61 2.49K 0.77 0.59 0.33 K 1.28 1.61 2.49A 0.77 0.59 0.33 A 1.28 1.61 2.49

Round 3: Low Med HighChoose 5%: 1.28 1.28 1.28

Heads: 1.28 1.61 2.49Tails: .88 .77 .59

Round 4:Low Medium High

5, 6, 7, 8, 9 1.28 1.61 2.49

2, 3, 4, 10, 11, 12 0.88 0.77 0.59

External Resources• http://www.financialliteracyfocus.org/edu.html

• http://www.mymoney.gov/myresources.html

• http://www.jumpstart.org/jump$tart-clearinghouse.html

• http://www.weseed.com/

• http://www.smartmoney.com/?link=SM_logo_home