Download Risk Quantification and Investment Decision-Making and more Exams Economics in PDF only on Docsity!
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Risk - - - correct answer ✅numerical measure about the future payoff to an investment assessed over some time horizon Risk vs uncertainty - - - correct answer ✅risk can be quantified (measured) uncertainty can not 5 characteristics of Risk - - - correct answer ✅1. risk can be quantified
- the riskier an investment the less desirable and the lower the price
- risk arises because the future outcomes are unknown
- we do not know which of many possible outcomes will follow in the future
- risk has to do with the future payoff of an investment
- we Mesut imagine all the possible payoffs and the likelihood of each
- risk must be assessed over some time horizon
- in general, risk over shorter periods is lower
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- risk usually measured relative to some benchmark, not in isolation
- frequently investments are compare to a "risk free rate" like US treasury bonds if an investment will return $1600, 25% of the time and $700, 75% of the time what is the expected value of the investment - - - correct answer ✅.25 x 1600 = 400 .75 x 700 = 525 EV = 925 a risk free asset is - - - correct answer ✅an investment whose future value is known with certainty and whose return is the risk free rate of return
- the payoff you receive is guaranteed and cannot vary variance - - - correct answer ✅average of the square deviations of the possible outcomes from their expected value, weighted by their probabilities
- compute expected value
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*** risk free investments have rates of return a. equal to zero b. with a std dev equal to zero c. that are uncertain but have a time horizon d. exhibit a large spread of potential payoffs (super risky) - - - correct answer ✅B. with standard deviations equal to zero risk aversion - - - correct answer ✅most people do not like risk and will pay to avoid it because most of us are risk adverse
- a risk adverse investor will always prefer an investment with a certain return to one with the same expected return but with any amount of uncertainty therefore the riskier an investment the higher the risk premuim risk premium - - - correct answer ✅the compensation investors require to hold a risky asset
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idiosyncratic risk - - - correct answer ✅- (or unique risks) are those that affect a small number of people but no one else
- an individual car accident
- a company makes a bad investment decision systematic risk - - - correct answer ✅risks that affect the whole economy
- 9/11 or financial crisis diversion - - - correct answer ✅risk can be reduced through diversification or holding more than one risk at a time
- this reduces idiosyncratic risk but not systematic -- why? --- everything is affected w/ systematic risk because it involves the broader economy one can hedge risks or spread them among many investments hedging risk - - - correct answer ✅strategy to reducing the idiosyncratic risk by making two investments with opposing risks
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- half the time : loses 5% - - - correct answer ✅EV= .5 (10%) + .5 (- 5%) = 2.5% VAR = .5(10-2.5) + .5(-5 - 2.5) = 56.25%^ SD = SQ RT (56.25) = 7.5% Invest $ EV = .5 (3300) + .5( 2850) = $ SD = 7.5% = (3000 x 7.5%) = $
investment A returns 10% half the time and -15% half the time
- if u paid $1000 for this investment what is EV and SD in % - - - correct answer ✅. 5 ( 10) + .5 (-15) = -2.5% (10 + 2.5) = 12.5 ^2 = 156. (-15 + 2.5) = -12.5 ^2 = 156. .5 (156.25) + .5 (156.25) 78.125 + 78.125 = 156. sq rt of 156.25 = 12.5 = SD
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portfolio return - - - correct answer ✅the expected return on a portfolio is weighted average of the individual expected returns
- the risk of a portfolio depends on the correlation (relationships) between the returns of the components a portfolio is composed of 2 stocks (A, B) with SD = 6.5% and 13%. If A is 25% of the portfolio and B is 75% and the correlation is .5.
- What is the portfolio SD - - - correct answer ✅VAR = .25^2 (6.5)^
- .75^2 (13)^2 + 2 (.25)(.75)(6.5)(13)(.5) VAR = 113. SD = sq rt 113.54 = 10. Value at Risk (VaR) - - - correct answer ✅- the worst possible outcome
- we can use the ideas of diversification along with historical correlations between investments to calculate what is known as value at risk
- financial institutions use value at risk (VaR) as a common measure of the riskiness of the business
- VaR answers the question: How much will I lose if the worst possible scenario occurs?
- 99.7% of events should be <3 SD
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SD of individual stock = 15% SD of market is = 10% 1 x (.15/.10) = 1.
- perfect correlation: If the market goes up 10% stock tends to go up 15 % correlation =. SD individual = 30% SD market = 10% .5 x (.30/.10) = 1.
- your current portfolio has SD = 11%
- considering adding another investment with SD = 14%
- and a correlation of. what is the beta relative to your current portfolio? what would your portfolio SD equal if 10% of your portfolio is the new investment? - - - correct answer ✅Beta = .30 x ( .14/.11) =. VAR = (.11)^2 (.90)^2 + (14)^2(.10)^2 + 2 (.11)(.90)(.14)(.10)(.30)
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SD = 108
sq rt 108 = 10.39% = portfolio SD Risk and expected return - - - correct answer ✅Rm = Rf + market risk premium
- where Rf = risk free return
- and the market risk premium is the compensation for taking on the market risk market risk premium = Rm -Rf Expected return on a security ( CAPM) - - - correct answer ✅Capital asset pricing model (CAPM) relates the expected return of an individual investment to its risk relative to the market Ri = Rf + B x (Rm - Rf) expected return on a security = risk free rate x beta of the security x market risk premium
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risk neutral - - - correct answer ✅- a risk neutral investor would choose to maximize the expected value (doesn't care about risk)
- we usually assume that a company will act as if it is risk neutral when making decisions (picking the highest NPV) expected utility hypothesis - - - correct answer ✅- the expected utility hypothesis describes how people make choices under uncertainty
- way of saying it Is not the dollars that matter but how happy those dollars will make you convex vs concave - - - correct answer ✅x^2 is a convex function sq rt of X is concave decreasing marginal utility of wealth - - - correct answer ✅in general we assume that people have concave utility functions because at a certain point , more money does not make people happier
suppose your utility function is the square root of dollars. what is your utility if you have $100? what is the marginal utility of an extra $100?
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a. 5, 10 b. 10, 14 c. 10, 4 d. 25 , 100 - - - correct answer ✅sq rt of $100 = 10 sq rt of 200 = 14. utility = 10 utility of extra 100 = an increase of 4. Ellsberg paradox - - - correct answer ✅- showed that most people do not behave as the expected utility hypothesis suggests
- one possible explanation is people dislike ambiguity (not knowing the fraction of black vs yellow) and choose the choice that has known probabilities
- people dislike ambiguity allais paradox - - - correct answer ✅- violation of expected utility is known as the allays paradox
- people like certainty and ignore small differences in probabilities
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stat with 50 and gain 50 end with $
- expected hypothesis theory says that someone should be indifferent between these, but most people would hate the first option of losing your money and would love the second option of doubling your money
prospect theory suggests that people will tend to... a. prefer to take risks no matter what b. prefer to avoid risks no matter what c. prefer to take risks to avoid losses but avoid risks for gains d. prefer risk for potential gains but avoid risks to avoid losses - - - correct answer ✅C Net Present Value (NPV) - - - correct answer ✅NPV = projects value
- estimate future cash flows
- choose appropriate discount rates
- find the present value of the cash flows
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- subtract initial investment
which one of the following will decrease NPV of a project a. an increase in discount rate b. increasing amount of initial cash investment c. having all future cash flows occur in the final year vs. evenly spaced over 5 years d. decreasing the final periods cash flow e. all of the above - - - correct answer ✅E. all of the above
investment A or B or C returns 10% half the time and 5% half the time (corr=0) if you invest in equal amounts of A,B,C, your risk will _____ relative to investing in just A. the SD of your portfolio will _____ as well. a. decrease, decrease, b. increase, increase c. decrease, increase
