Investment Risk Eric Higgins Department of Finance, KSU
Dec 31, 2015
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/m
odules/
• 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