RMI 2302 Exam 2 Review TEST 2 NYCE Module 6 Risk Reward Employers want employees who can make critical decisions Your education as a whole in the College of Business is about understanding the relationship between risk and reward Proper decision making implies that any individual organization or government willing to take on additional risk should be compensated with some type of additional reward In other words the level of risk should have a commensurate level of reward That risk reward trade off will differ among individuals depending on their level of risk aversion It will vary among organizations as well but not as much With organizations making decisions based on expected value rather than expected utility there is less variation in decision making Expected value has less variation But there are still differences in the risk reward trade off Some organizations are much more willing to take risk than others The expectation of these organizations is high risk high reward Other organizations prefer lower risk lower reward strategies Basis of Insurance People are willing to pay to avoid risk Individuals Measure risk and reward using expected utility They are risk averse and prefer the sure thing over uncertainty They ask the following questions how much reward is necessary to entice you to take risk and how much are you willing to pay to avoid risk Refer to the following expected utility example from Module 4 for this particular investment they needed an expected return of 25 to invest In other words for them to be willing to put their 4 for certain at risk they would expect to get 5 in return that is 1 more than they had 1 4 25 or 25 Example You have 5 You can either save it or invest it If you invest it there is a 50 chance you will make 4 end up with 9 and a 50 chance you will lose 4 end up with 1 Assume the utility function is the square root function of u x X 5 meaning XWhat should you do Calculate Expected Utility Based on expected utility the pillow option is the best option because it has the higher utils Individuals use expected utility Option 1 Save it Expected Utility P 1 Probability x Outcome 1 x 5 2 24 utils X 5 X Option 2 Invest it Expected Utility RMI 2302 Exam 2 Review X1 1 P1 5 Probability1 x Outcome1 Probability2 x Outcome2 5 x 1 5 x 9 2 utils X2 9 P2 5 X In this case the pillow has the higher utility value measure and we should pick that option Play around with the amounts of the outcome to see when the individual will flip and make an alternative decision trial and error What amount of wealth would an investor be indifferent Since we are dealing with a square root function what value has a square root of 2 4 The investor would be indifferent between 4 for certain equivalent or 50 50 chance of 9 In other words they would be willing to pay 1 to avoid the investment 5 4 1 If there is no saving option and you can only invest it would you rather do this or is there a way to avoid it Would you take 4 50 for sure meaning you are giving up losing 0 50 in order to avoid having to make the investment How about 4 25 How about 4 P 1 X1 4 50 X2 4 25 X3 4 X Since the utility of the investment is 2 utils we can calculate the following 1 x 4 50 2 12 utills yes we would be willing to pay 0 50 to avoid the risk 1 x 4 25 2 06 utills yes we would be willing to pay 0 75 to avoid the risk 1 x 4 2 utills at this point we are indifferent towards paying 1 to avoid and investing Organizations Measure risk and reward by using expected value CAPM and the Efficient Frontier There is no natural risk aversion but they do look at risk and their decisions do reflect risk When discussing risk and reward we use the terms opportunity cost aka cost of capital If you want me to put my money at risk how much are you willing to offer as a return on the investment Riskier Organizations higher cost of capital and a higher interest rate discount rate The cash flow does not change but the opportunity cost and discount rates do change Money today is worth more and is more valuable than future cash flows Most organizations project future cash flows from investments and other opportunities Organizations will discount those cash flows back to present value based on cost of capital Calculate Expected Value Based on expected value it does not matter Both options have an expected value of 5 Only organizations use expected value Option 1 Save it Expected Value P 1 Probability x Outcome 1 x 5 5 X 5 Option 2 Invest it Expected Value RMI 2302 Exam 2 Review P1 5 Probability1 x Outcome1 Probability2 x Outcome2 5 x 1 5 x 9 5 X2 9 X1 1 P2 5 Cost of Capital aka Opportunity cost can be utilized by organizations through discounting When you compare the value of investing a dollar today to the value of a dollar in the future you must discount or bring that future dollar back to a value today The higher the opportunity cost or cost of capital the larger the future value needs to be to get them to invest They estimate the future cash flows that are generated by an investment decision and then discount them back to present value That discount rate is the required reward necessary for the organization to take on risk Once all of the potential choices are analyzed then the organization can make an informed decision about which way they want to go Cost of Capital is commensurate with the riskiness of the firm CAPM The Capital Asset Pricing Model only reward systemic risk and not worried about diversifiable risk These risks affect the entire portfolio This formula shows the exact tradeoff and tells you what the return is on any given asset using rA rF B rM rF RA the risk of a given asset RF the risk free rate return of safest investment B Beta overall effect of my stock with the market RM return of the overall market return Diversifiable Risk If you can diversify there is no risk and the net position won t change 27 stocks is a diversified portfolio of stocks Efficient Frontier a graph that shows the tradeoff between risk and reward The Efficient Frontier line represents the optimal combination of risk and return Each dot represents a portfolio The dots that are closest to the Efficient Frontier line are the portfolios that are expected to show the best performance with the smallest risk Vertical axis expected return Horizontal axis risk volatility standard deviation As risk gets greater reward has to get greater You cannot be to the left of the line You cannot be more efficient than …
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