1. Ch12. Risk, Capital Budgeting and Diversification Goals: Five major statistical measures Risk-adjusted discount rate Three alternative techniques for incorporating risk into the analysis Diversification Portfolio Risk Measure

2. 1. Review of some useful statistical concepts 1) Expected Value: a weighted average of all possible outcomes where the weights are the probabilities of occurrence. Built-in-function: array commend

3. 2) Variance and Standard Deviation In finance, risk is measured by standard deviation and variance. Average deviation from the mean. Built-in function : VarP (population) and Var (sample)

4. Built-in function for SD: SQRT(Var) STDEVP or STDEV

5. 3) Coefficient of Variance To deal with the scale problem in standard deviation Def of Scale Problem: though the probability of loss is same, the changing scale causes to increase variance or SD

6. 4) Charting the Probability Distribution Using histogram, we can create the distribution table. 2. Incorporating Risk into Capital Budgeting Decisions WACC is a discount rate applied to projects which have an average level of risk for the firm. What we have to do with projects with a higher and lower level of risk?

7. 1) Risk Adjusted Discount Rate (RADR) RADR = WACC + Risk Premium Still Premium is subjective. Ex) VLOOKUP(Lookup_Value, Table_Array, Col_Index_Num, Range_Lookup) Here, Lookup : the number that you want to find, Table_Array: the location of table, Col_Index: the number of column that you want to pill data, Range: approximate or exact match

8. 2) Alternative to the RADR RADR’s problem: - Risk is assumed to be an increasing function of time. But how about specified cash flows? 2-1) Certainty-equivalent (CE) approach To adjusted risk, it reduce the cash flows Multiply the cash flow by the certainty equivalent coefficient (CE coefficient)

9. How to calculate CE coefficient, = Riskless cash flow/ risk cash flow. Ex) you are willing to accept $95 dollars for sure in place of a risky $100 one year from now. CE coefficient = 95/100 = 0.95 Ex) How to calculate NPV with CE coefficient

10. - Cash flow * CE coefficient - Discount by a risk free rate 2-2) Decision Tree Approach Graphical depiction of the potential cash flows and associated probabilities Four steps in a decision tree - Conditional probability distribution for each period

11. Joint probability for each potential path NPV for each path Expected NPV, using probability 3. Portfolio Return and Risks Portfolio will reduce total risks. 3-1) Portfolio Return

12. 3-2) Portfolio Risks Portfolio Risk will be influenced by weights and number of securities. Portfolio with two stocks

13. 3-3) How to set up weights in portfolios Setting up a portfolio table Using solver – minimizing a risk or maximizing a return