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# Risk Concept And Management 5

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### Risk Concept And Management 5

1. 1. Concept and Management of Risk
2. 2. Concept of Probability <ul><li>Outcome and Decision </li></ul><ul><ul><li>Outcome </li></ul></ul><ul><ul><ul><li>Driven by “nature”, out of our control </li></ul></ul></ul><ul><ul><ul><li>Can only wait for the event to happen to see the outcome </li></ul></ul></ul><ul><ul><li>Decision </li></ul></ul><ul><ul><ul><li>Driven by us, in our control </li></ul></ul></ul><ul><ul><ul><li>We decide the outcome, based on knowledge of outcomes </li></ul></ul></ul><ul><li>Class of outcomes (event) </li></ul><ul><li>Probability of a particular outcome of an event </li></ul><ul><ul><li>If the event (class) is allowed to happen a very large number of times, the fraction of the total number of incidents in which the result is a particular outcome is the probability of that outcome </li></ul></ul><ul><li>Sum of probabilities of an event (class) is 100% </li></ul>
3. 3. Concept of Risk <ul><li>Risk of an outcome : Probability weighted “Loss” expected of the outcome class </li></ul><ul><li>Probability of and amount by which, a net positive cash-flow is expected to turn out to be less than earlier expected. </li></ul><ul><li>Risk=probability of accident * loss in accident </li></ul><ul><li>Risk v/s Uncertainty </li></ul><ul><li>Systematic and Unsystematic Risk </li></ul>
4. 4. Concept of Risk: example <ul><ul><li>Example: </li></ul></ul><ul><ul><ul><li>Mangoes cost 120Rs. (per dozen). Of our purchase done in one single lot, some would go bad and be non-saleable. If weather is unsuitable (5% probability) almost 50% go bad. Most probably (90%probability) around 10% of the quantity will go bad. Otherwise, only if we are very lucky (balance 5%), just 1% will go bad. Then, as we sell them over the three month season, in the first month, they will sell most probably (80% chance) at a price of 200Rs. But depending on unexpected fierce competition, it could just be Rs.150. In the second month, the market stabilizes (90% chance) to a price of Rs.160, with excessive competition possibly driving it to Rs. 130. What is the “risk” of the decision to buy 100 dozen for sale? </li></ul></ul></ul>
5. 5. Systematic and Unsystematic Risks <ul><li>Systematic risk </li></ul><ul><ul><li>refers to the movements of the whole market </li></ul></ul><ul><ul><li>Residual risk even with a market portfolio </li></ul></ul><ul><ul><li>Expected or calculable on historical study </li></ul></ul><ul><li>Unsystematic (Idiosyncratic, specific) </li></ul><ul><ul><li>The risk of price change due to the unique circumstances of a specific security, as opposed to the overall market. </li></ul></ul><ul><ul><li>Virtually eliminated in a diversified portfolio </li></ul></ul><ul><li>Investors only get rewarded for taking on systematic risk. Unsystematic risk can be diversified away, so the market does not offer higher return for taking it on. </li></ul><ul><li>Expected return on security R security = R f + m + ε </li></ul><ul><ul><li>R f is the riskfree return expectation </li></ul></ul><ul><ul><li>m is systematic risk premium </li></ul></ul><ul><ul><li>ε is unsystematic risk of security premium </li></ul></ul>
6. 6. The Decision Tree : Elements <ul><li>The Decision Tree </li></ul><ul><ul><li>consists of decision nodes, event nodes and terminal nodes connected by branches. </li></ul></ul><ul><li>Nodes </li></ul><ul><ul><li>Decision Nodes </li></ul></ul><ul><ul><li>Event Nodes </li></ul></ul><ul><ul><li>Terminal Nodes </li></ul></ul><ul><li>Branches </li></ul><ul><ul><li>Mutually exclusive and collectively exhaustive </li></ul></ul><ul><li>Probability of a Branch </li></ul><ul><ul><li>Only for each branch emanating from an event node </li></ul></ul><ul><ul><li>“ Probability” of the outcome being that particular branch. </li></ul></ul>terminal value endpoint ◄ Terminal event branches circle ● Event decision branches square ■ Decision Node Successor Written Symbol Type of Node
7. 7. Decision Tree : Graphic <ul><li>A manager of a factory making product B has to decide to invest in development for a new product - product A or product C. She cannot do both due to budget constraints. Product A is estimated to require two million dollars of R&D investment, but only has a 50% chance of the research being successful and a product being obtained. It will have a 30% chance of selling \$5M profit, a 40% chance of selling \$10M profit, and a 30% chance of no sales. Product C, on the other hand, will also cost \$2M in R&D but has an 80% chance of selling \$5M profit and a 20% chance of no sales. \$1M is the manufacturing cost for either product. </li></ul>
8. 8. The Decision Tree: Values <ul><li>Cash flow of a Branch </li></ul><ul><ul><li>Cash Flow expected simply due to the action of taking the branch. </li></ul></ul><ul><li>Values of Nodes </li></ul><ul><ul><li>Value of a Terminal Node (“Payoff” or Terminal value) </li></ul></ul><ul><ul><ul><li>sum the cash flow values of all the branches leading to the terminal node </li></ul></ul></ul><ul><ul><li>Value of an Event Node (Expected Value EV or Rollback value) </li></ul></ul><ul><ul><ul><li>Probability weighted sum of values of branches starting from the node </li></ul></ul></ul><ul><ul><li>Value of a Decision Node (Expected Value EV or Rollback value) </li></ul></ul><ul><ul><ul><li>Value of the branch starting from the node having the highest positive cash flow among all branches starting from the node </li></ul></ul></ul><ul><li>Value of a Branch </li></ul><ul><ul><li>Value of the end node of the branch </li></ul></ul><ul><ul><li>Not the same as the “Cash Flow” of a branch </li></ul></ul>
9. 9. The Decision Tree : An example <ul><li>Drivetek Inc. is evaluating a tender for a fee of \$250,000 offered for the best proposal for developing the new storage device. Management estimates a cost of \$50,000 to prepare a proposal with a fifty-fifty chance of winning the contract. However, DriveTek's engineers have two alternative approaches for building the product. The first approach is a mechanical method with a cost of \$120,000. A second approach involves electronic components and will cost only \$50,000 to develop a model, but with only a 50 percent chance of satisfactory results. </li></ul><ul><li>There are two major decisions in the DriveTek problem. First, the company must decide whether or not to prepare a proposal. Second, if it prepares a proposal and is awarded the contract, it must decide which of the two approaches to try to satisfy the contract. </li></ul><ul><li>Credits: Treeplan Inc. </li></ul>
10. 10. The Decision Tree : Example
11. 11. The Decision Tree : Example <ul><li>Terminal Values, Rollback EVs, Choice Indicators </li></ul>
12. 12. The Decision Tree : Example <ul><li>Decision 1: </li></ul><ul><ul><li>The NPV of decision node 1 is the value of the “Prepare proposal” branch (\$20,000). Hence it is advisable to make the proposal. </li></ul></ul><ul><li>Decision 2: </li></ul><ul><ul><li>If we are awarded the contract, it is required to make the decision 2. </li></ul></ul><ul><ul><li>The NPV of decision 2 is the value of the “Use electronic method” and hence if we get the contract, we should use the electronic method to fulfil it. </li></ul></ul>
13. 13. Sensitivity Analysis <ul><li>Sensitivity (“what if” or “bop”) </li></ul><ul><ul><li>How does output vary with change in input </li></ul></ul><ul><ul><li>Theoretically ∂ (Cashflow NPV) / ∂ factor i </li></ul></ul><ul><li>Mechanism </li></ul><ul><ul><li>List all factors F i affecting output NPV </li></ul></ul><ul><ul><li>List Optimistic, Realistic and Pessimistic values for each factor F i </li></ul></ul><ul><ul><li>Evaluate Output (NPV) for each possibility </li></ul></ul><ul><ul><li>Inspect the resultant table for sensitivity </li></ul></ul>
14. 14. Sensitivity Analysis : Example <ul><li>Jet engine manufacturer considers a project with expected cash flows as discussed in Ross et al Sec. 8.2 page 214 (all values in M\$). </li></ul><ul><ul><li>Initial investment I = 1500, depreciated on a straight-line basis over 5 years, so yearly depreciation = 300 </li></ul></ul><ul><ul><li>Revenues in years 1to5 of 6000 (market size S 10000 units, market share M 30%, unit price of 2), variable cost V 3000 (unit cost 1), and annual fixed cost F=1791 </li></ul></ul><ul><ul><li>Corporate tax rate of 34% , and appropriate discount rate of 15% </li></ul></ul><ul><li>Output = NPV= ((M*S*(P-U) - F)*(1-T) + T*I/5) * A 5,15% - I </li></ul><ul><li>Input factors : </li></ul><ul><ul><li>Market Share M </li></ul></ul><ul><ul><li>Size of Market S </li></ul></ul><ul><ul><li>Price per Engine P. </li></ul></ul><ul><ul><li>Variable unit cost U </li></ul></ul><ul><ul><li>Fixed Cost (per period) F </li></ul></ul><ul><ul><li>Investment I </li></ul></ul><ul><li>List Pessimistic, Realistic and Optimistic values for each input factor. </li></ul><ul><li>Create a table of NPV’s with each input factor in turn allowed to take on its range of values, keeping all other factors at their realistic value </li></ul>
15. 15. Sensitivity Analysis : Example <ul><li>Realistic estimate for all input factors at realistic values: </li></ul><ul><li>Annual Cash flow </li></ul><ul><ul><li>Annual taxable income </li></ul></ul><ul><ul><li>= revenue - costs (expenses) - depreciation </li></ul></ul><ul><ul><li>= ( price*sales ) - ( variable costs + fixed costs ) - depreciation </li></ul></ul><ul><ul><li>= (2*3000) - (3000 + 1791) – 1500/5 = 909 </li></ul></ul><ul><ul><li>Tax = 0.34 * 909 = 309 </li></ul></ul><ul><ul><li>Net income = 909 - </li></ul></ul><ul><ul><li>Annual Cash flow </li></ul></ul><ul><ul><li>= (net income) + (depreciation) </li></ul></ul><ul><ul><li>= ( 1 - TC ) * ( revenues - expenses - depreciation )+ ( depreciation ) </li></ul></ul><ul><ul><li>= (909 - 309) + 300 = 900 </li></ul></ul><ul><li>Cash flow is (-1500, 900, 900, 900, 900, 900) </li></ul><ul><li>NPV = -1500 + A 5,15% * 90 = 1517 </li></ul>
16. 16. Sensitivity Analysis : Example <ul><li>BOP values for factors and NPV sensitivity </li></ul>
17. 17. Sensitivity Analysis <ul><li>Advantages </li></ul><ul><ul><li>Sensitivity shows up the impact on NPV of an error in estimating each input factor. </li></ul></ul><ul><ul><li>Sensitivity shows which input factor needs to be studied in more detail </li></ul></ul><ul><ul><ul><li>The NPV table can also indicate assumptions having the biggest effect on NPV and where more detailed investigation is required </li></ul></ul></ul><ul><ul><ul><li>A wide range of NPV’s, with many large negative and positive values, should make reinvestigate those cases </li></ul></ul></ul>
18. 18. Operating Leverage as Sensitivity <ul><li>Operating Leverage: </li></ul><ul><ul><li>The degree to which a project relies on fixed costs </li></ul></ul><ul><ul><li>Degree of operating leverage = % change in OCF relative to % change in quantity sold </li></ul></ul><ul><ul><li>DOL = 1 + (FC/OCF) </li></ul></ul><ul><ul><ul><li>FC=Fixed cost, OCF=Operational Cash Flow </li></ul></ul></ul><ul><ul><li>Eg. If OCF is Rs.30,000 for 14000 units and FC=Rs. 40,000, DOL = 1 + (40,000/30,000) =2.333. Thus a 1% increase in units sold would generate a 2.33% increase in OCF in the base case range. Vice versa, a 1% decrease in sales = 2.33% decrease in OCF. </li></ul></ul>
19. 19. Scenario Analysis <ul><li>Ask basic “What if?” questions and rework NPV estimates </li></ul><ul><li>Worst case—good start point—what is the minimum NPV for the project? </li></ul><ul><li>Best case—upper limit bound of project NPV </li></ul><ul><li>Base case—most likely outcome assumed (probably some midpoint between best & worst) </li></ul>
20. 20. Monte-Carlo Simulation <ul><li>Project Analysis as a gambling strategy </li></ul><ul><li>Steps: </li></ul><ul><ul><li>Specify Basic Model (Revenues, Costs,…) </li></ul></ul><ul><ul><li>Specify probability distribution of output (cashflow) over values of each input variable </li></ul></ul><ul><ul><li>Generate cashflow for 1 set of parameter values </li></ul></ul><ul><ul><li>Repeat above step large no. of times with input values chosen according to their probabilities </li></ul></ul><ul><ul><li>Calculate project NPV as a probability weighted average of above cashflows. </li></ul></ul>
21. 21. Normal Distribution
22. 22. Monte Carlo: pros and cons <ul><li>Advantages </li></ul><ul><ul><li>Need to build precise model deepens understanding of the project </li></ul></ul><ul><ul><li>Interactions between atomic variables expressly understood and specified </li></ul></ul><ul><li>Disadvantages </li></ul><ul><ul><li>Difficult to model the precise relationships </li></ul></ul><ul><ul><li>Difficult to define probability distributions </li></ul></ul><ul><ul><li>Computed output is devoid of practical intuition </li></ul></ul><ul><li>Not widely used </li></ul>
23. 23. CAPM: Capital Asset Pricing Model <ul><li>E(R i ) = R f + β im * (E(R m ) – R f ) </li></ul><ul><li>Where </li></ul><ul><li>E(R i ) is the expected return on the capital asset </li></ul><ul><li>R f is the risk-free rate of interest </li></ul><ul><ul><li>As the arithmetic average of historical risk free rates of return and not the current risk free rate of return </li></ul></ul><ul><li>R m is the expected return on the market portfolio </li></ul><ul><li>β im , “ beta coefficient” is the sensitivity of the asset returns to market returns (R market – R riskfree ) is sometimes known as the market premium or risk premium (the difference between the expected market rate of return and the risk-free rate of return) </li></ul>
24. 24. CAPM
25. 25. The Beta in CAPM <ul><li>β im = Cov (R i , R m )/Var(R f ), where </li></ul><ul><ul><li>R i is the expected return on the capital asset </li></ul></ul><ul><ul><li>R m is the expected return of the market the expected market rate of return is usually measured by looking at the arithmetic average of the historical returns on a market portfolio </li></ul></ul><ul><li>What does Beta mean or imply? </li></ul><ul><ul><li>A beta of 1 implies the asset has the same systematic risk as the overall market </li></ul></ul><ul><ul><li>A beta < 1 implies the asset has less systematic risk than the overall market </li></ul></ul><ul><ul><li>A beta > 1 implies the asset has more systematic risk than the overall market </li></ul></ul><ul><ul><li>A beta = 0 implies the asset is a risk-free asset </li></ul></ul>
26. 26. Factors Affecting Expected Return <ul><li>Pure time value of money – measured by the risk-free rate </li></ul><ul><li>Reward for bearing systematic risk – measured by the market risk premium </li></ul><ul><li>Amount of systematic risk – measured by beta </li></ul>
27. 27. Capital Gains <ul><li>Rise of value of Capital Investment </li></ul><ul><li>Capital Gain = (P t+1 – P t ). %Capital Gain = (P t+1 – P t ) /P t </li></ul><ul><li>Long Term and Short Term Capital Gains </li></ul><ul><ul><li>LT : if asset held for >36 (12*) months </li></ul></ul><ul><ul><li>ST : if asset held for <36 (12*) months </li></ul></ul><ul><ul><li>* : shares, UTI units, MFunits, listed securities (covered by STT) </li></ul></ul><ul><li>Indexing of Capital Gain for Inflation </li></ul><ul><li>Capital Loss and Net Capital Gain </li></ul><ul><li>Taxation on Capital Gains </li></ul><ul><ul><li>Others : 20% on LTG and full rate on STG </li></ul></ul><ul><ul><li>Equity Capital : 10% ST, nil (+STT) : LT </li></ul></ul><ul><ul><li>Mutual Funds exempt from Capital Gains tax at hands of unit-holders </li></ul></ul>
28. 28. Indexing of a Capital Gain <ul><li>Cost Inflation Index </li></ul><ul><li>Capital Gain </li></ul><ul><ul><li>= Full value of consideration </li></ul></ul><ul><ul><li>- Indexed cost of acquisition </li></ul></ul><ul><li>Indexed cost of acquisition = </li></ul><ul><ul><li>= Cost of acquisition </li></ul></ul><ul><ul><li>x CII* of year of transfer </li></ul></ul><ul><ul><li>/ CII of year of acquisition </li></ul></ul>
29. 29. Capital Gains: example <ul><li>Example: </li></ul><ul><ul><li>'A' an individual sells a residential house on 12.4.2000 for Rs. 25,00,000/-. The house was purchased by him on 5.7.1997 for Rs. 5,00,000/-. </li></ul></ul><ul><ul><li>Since 'A' has held the capital asset for less than 36 months, it is a short capital asset for him and its transfer gives rise to short term capital gains. </li></ul></ul><ul><ul><li>Indexed cost of acquisition </li></ul></ul><ul><ul><li>= 25,00,000 * 389 / 305 = 6,37,705 Rs. </li></ul></ul><ul><ul><li>Taxable Short Term Capital Gain = Rs. 18,62,295 </li></ul></ul>
30. 30. The lighter side: I never take a risk <ul><li>When I come from office in the evening, my wife is cooking I can hear the noise of utensils in the kitchen. </li></ul><ul><li>I stealthily enter the house and take out the bottle from my black cupboard. </li></ul><ul><li>Shivaji Maharaj is looking at me from the photo frame </li></ul><ul><li>But still no one is aware of it because I never take a risk </li></ul><ul><li>I take out the glass from the rack above the old sink and quickly enjoy one peg, then wash the glass and again keep it on the rack. </li></ul><ul><li>Of course I also keep the bottle inside my cupboard </li></ul><ul><li>Shivaji Maharaj is giving a smile   </li></ul><ul><li>I peep into the kitchen. My wife is cutting potatoes </li></ul><ul><li>But still no one is aware of what I did Becoz I never take a risk </li></ul><ul><li>I: Any news on Iyer's daughter's marriage </li></ul><ul><li>Wife: Nope, she doesn't seem to be that lucky. Still they are looking out for her </li></ul><ul><li>I again come out; there is a small noise of the black cupboard </li></ul><ul><li>But I don't make any sound while taking out the bottle </li></ul><ul><li>… contd </li></ul>
31. 31. I never take a risk (2of3) <ul><li>… contd. </li></ul><ul><li>I take out the glass from the old rack above sink </li></ul><ul><li>Quickly enjoy one peg, Wash the bottle and keep it in the sink </li></ul><ul><li>Also keep the Black Glass in the cupboard </li></ul><ul><li>But still no one is aware of what I did </li></ul><ul><li>Becoz I never take a risk   </li></ul><ul><li>I: But still I think Iyer's daughter's age is not that much </li></ul><ul><li>Wife: What are you saying? She is 28 yrs old... like an aged horse </li></ul><ul><li>I:(I forgot her age is 28) Oh Oh... </li></ul><ul><li>I again take out potatoes out from my black cupboard </li></ul><ul><li>But the cupboard's place has automatically changed </li></ul><ul><li>I take out the bottle from the rack and quickly enjoy one peg in the sink </li></ul><ul><li>Shivaji Maharaj laughs loudly </li></ul><ul><li>I keep the rack in the potatoes & wash Shivaji Maharaj's photo & keep it in the black cupboard Wife is keeping the sink on the stove But still no one is aware of what I did Becoz I never take a risk </li></ul><ul><li>… contd. </li></ul>
32. 32. I never take a risk (3of3) <ul><li>… contd. </li></ul><ul><li>I: (getting angry) you call Mr. Iyer a horse? If you say that again, I will cut your tongue...! Wife: Don't just blabber something, go out and sit quietly... </li></ul><ul><li>I take out the bottle from the potatoes Go in the black cupboard and enjoy a peg Wash the sink and keep it over the rack </li></ul><ul><li>Wife is giving a smile Shivaji Maharaj is still cooking But still no one is aware of what I did Becoz I never take a risk   I: (laughing) So Iyer is marrying a horse!! Wife: Hey go and sprinkle some water on your face...   I again go to the kitchen, and quietly sit on the rack Stove is also on the rack. </li></ul><ul><li>There is a small noise of bottles from the room outside I peep and see that wife is enjoying a peg in the sink But none of the horses are aware of what I did </li></ul><ul><li>Becoz Shivaji Maharaj never takes a risk </li></ul><ul><li>Iyer is still cooking. And I am looking at my wife from the photo and laughing… </li></ul>
33. 33. Interactive Session