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Risk Concept And Management 5

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FINANCE,CFM

FINANCE,CFM

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    • 1. Concept and Management of Risk
    • 2. Concept of Probability
      • Outcome and Decision
        • Outcome
          • Driven by “nature”, out of our control
          • Can only wait for the event to happen to see the outcome
        • Decision
          • Driven by us, in our control
          • We decide the outcome, based on knowledge of outcomes
      • Class of outcomes (event)
      • Probability of a particular outcome of an event
        • 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
      • Sum of probabilities of an event (class) is 100%
    • 3. Concept of Risk
      • Risk of an outcome : Probability weighted “Loss” expected of the outcome class
      • Probability of and amount by which, a net positive cash-flow is expected to turn out to be less than earlier expected.
      • Risk=probability of accident * loss in accident
      • Risk v/s Uncertainty
      • Systematic and Unsystematic Risk
    • 4. Concept of Risk: example
        • Example:
          • 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?
    • 5. Systematic and Unsystematic Risks
      • Systematic risk
        • refers to the movements of the whole market
        • Residual risk even with a market portfolio
        • Expected or calculable on historical study
      • Unsystematic (Idiosyncratic, specific)
        • The risk of price change due to the unique circumstances of a specific security, as opposed to the overall market.
        • Virtually eliminated in a diversified portfolio
      • 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.
      • Expected return on security R security = R f + m + ε
        • R f is the riskfree return expectation
        • m is systematic risk premium
        • ε is unsystematic risk of security premium
    • 6. The Decision Tree : Elements
      • The Decision Tree
        • consists of decision nodes, event nodes and terminal nodes connected by branches.
      • Nodes
        • Decision Nodes
        • Event Nodes
        • Terminal Nodes
      • Branches
        • Mutually exclusive and collectively exhaustive
      • Probability of a Branch
        • Only for each branch emanating from an event node
        • “ Probability” of the outcome being that particular branch.
      terminal value endpoint ◄ Terminal event branches circle ● Event decision branches square ■ Decision Node Successor Written Symbol Type of Node
    • 7. Decision Tree : Graphic
      • 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.
    • 8. The Decision Tree: Values
      • Cash flow of a Branch
        • Cash Flow expected simply due to the action of taking the branch.
      • Values of Nodes
        • Value of a Terminal Node (“Payoff” or Terminal value)
          • sum the cash flow values of all the branches leading to the terminal node
        • Value of an Event Node (Expected Value EV or Rollback value)
          • Probability weighted sum of values of branches starting from the node
        • Value of a Decision Node (Expected Value EV or Rollback value)
          • Value of the branch starting from the node having the highest positive cash flow among all branches starting from the node
      • Value of a Branch
        • Value of the end node of the branch
        • Not the same as the “Cash Flow” of a branch
    • 9. The Decision Tree : An example
      • 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.
      • 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.
      • Credits: Treeplan Inc.
    • 10. The Decision Tree : Example
    • 11. The Decision Tree : Example
      • Terminal Values, Rollback EVs, Choice Indicators
    • 12. The Decision Tree : Example
      • Decision 1:
        • The NPV of decision node 1 is the value of the “Prepare proposal” branch ($20,000). Hence it is advisable to make the proposal.
      • Decision 2:
        • If we are awarded the contract, it is required to make the decision 2.
        • The NPV of decision 2 is the value of the “Use electronic method” and hence if we get the contract, we should use the electronic method to fulfil it.
    • 13. Sensitivity Analysis
      • Sensitivity (“what if” or “bop”)
        • How does output vary with change in input
        • Theoretically ∂ (Cashflow NPV) / ∂ factor i
      • Mechanism
        • List all factors F i affecting output NPV
        • List Optimistic, Realistic and Pessimistic values for each factor F i
        • Evaluate Output (NPV) for each possibility
        • Inspect the resultant table for sensitivity
    • 14. Sensitivity Analysis : Example
      • Jet engine manufacturer considers a project with expected cash flows as discussed in Ross et al Sec. 8.2 page 214 (all values in M$).
        • Initial investment I = 1500, depreciated on a straight-line basis over 5 years, so yearly depreciation = 300
        • 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
        • Corporate tax rate of 34% , and appropriate discount rate of 15%
      • Output = NPV= ((M*S*(P-U) - F)*(1-T) + T*I/5) * A 5,15% - I
      • Input factors :
        • Market Share M
        • Size of Market S
        • Price per Engine P.
        • Variable unit cost U
        • Fixed Cost (per period) F
        • Investment I
      • List Pessimistic, Realistic and Optimistic values for each input factor.
      • 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
    • 15. Sensitivity Analysis : Example
      • Realistic estimate for all input factors at realistic values:
      • Annual Cash flow
        • Annual taxable income
        • = revenue - costs (expenses) - depreciation
        • = ( price*sales ) - ( variable costs + fixed costs ) - depreciation
        • = (2*3000) - (3000 + 1791) – 1500/5 = 909
        • Tax = 0.34 * 909 = 309
        • Net income = 909 -
        • Annual Cash flow
        • = (net income) + (depreciation)
        • = ( 1 - TC ) * ( revenues - expenses - depreciation )+ ( depreciation )
        • = (909 - 309) + 300 = 900
      • Cash flow is (-1500, 900, 900, 900, 900, 900)
      • NPV = -1500 + A 5,15% * 90 = 1517
    • 16. Sensitivity Analysis : Example
      • BOP values for factors and NPV sensitivity
    • 17. Sensitivity Analysis
      • Advantages
        • Sensitivity shows up the impact on NPV of an error in estimating each input factor.
        • Sensitivity shows which input factor needs to be studied in more detail
          • The NPV table can also indicate assumptions having the biggest effect on NPV and where more detailed investigation is required
          • A wide range of NPV’s, with many large negative and positive values, should make reinvestigate those cases
    • 18. Operating Leverage as Sensitivity
      • Operating Leverage:
        • The degree to which a project relies on fixed costs
        • Degree of operating leverage = % change in OCF relative to % change in quantity sold
        • DOL = 1 + (FC/OCF)
          • FC=Fixed cost, OCF=Operational Cash Flow
        • 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.
    • 19. Scenario Analysis
      • Ask basic “What if?” questions and rework NPV estimates
      • Worst case—good start point—what is the minimum NPV for the project?
      • Best case—upper limit bound of project NPV
      • Base case—most likely outcome assumed (probably some midpoint between best & worst)
    • 20. Monte-Carlo Simulation
      • Project Analysis as a gambling strategy
      • Steps:
        • Specify Basic Model (Revenues, Costs,…)
        • Specify probability distribution of output (cashflow) over values of each input variable
        • Generate cashflow for 1 set of parameter values
        • Repeat above step large no. of times with input values chosen according to their probabilities
        • Calculate project NPV as a probability weighted average of above cashflows.
    • 21. Normal Distribution
    • 22. Monte Carlo: pros and cons
      • Advantages
        • Need to build precise model deepens understanding of the project
        • Interactions between atomic variables expressly understood and specified
      • Disadvantages
        • Difficult to model the precise relationships
        • Difficult to define probability distributions
        • Computed output is devoid of practical intuition
      • Not widely used
    • 23. CAPM: Capital Asset Pricing Model
      • E(R i ) = R f + β im * (E(R m ) – R f )
      • Where
      • E(R i ) is the expected return on the capital asset
      • R f is the risk-free rate of interest
        • As the arithmetic average of historical risk free rates of return and not the current risk free rate of return
      • R m is the expected return on the market portfolio
      • 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)
    • 24. CAPM
    • 25. The Beta in CAPM
      • β im = Cov (R i , R m )/Var(R f ), where
        • R i is the expected return on the capital asset
        • 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
      • What does Beta mean or imply?
        • A beta of 1 implies the asset has the same systematic risk as the overall market
        • A beta < 1 implies the asset has less systematic risk than the overall market
        • A beta > 1 implies the asset has more systematic risk than the overall market
        • A beta = 0 implies the asset is a risk-free asset
    • 26. Factors Affecting Expected Return
      • Pure time value of money – measured by the risk-free rate
      • Reward for bearing systematic risk – measured by the market risk premium
      • Amount of systematic risk – measured by beta
    • 27. Capital Gains
      • Rise of value of Capital Investment
      • Capital Gain = (P t+1 – P t ). %Capital Gain = (P t+1 – P t ) /P t
      • Long Term and Short Term Capital Gains
        • LT : if asset held for >36 (12*) months
        • ST : if asset held for <36 (12*) months
        • * : shares, UTI units, MFunits, listed securities (covered by STT)
      • Indexing of Capital Gain for Inflation
      • Capital Loss and Net Capital Gain
      • Taxation on Capital Gains
        • Others : 20% on LTG and full rate on STG
        • Equity Capital : 10% ST, nil (+STT) : LT
        • Mutual Funds exempt from Capital Gains tax at hands of unit-holders
    • 28. Indexing of a Capital Gain
      • Cost Inflation Index
      • Capital Gain
        • = Full value of consideration
        • - Indexed cost of acquisition
      • Indexed cost of acquisition =
        • = Cost of acquisition
        • x CII* of year of transfer
        • / CII of year of acquisition
    • 29. Capital Gains: example
      • Example:
        • '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/-.
        • 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.
        • Indexed cost of acquisition
        • = 25,00,000 * 389 / 305 = 6,37,705 Rs.
        • Taxable Short Term Capital Gain = Rs. 18,62,295
    • 30. The lighter side: I never take a risk
      • When I come from office in the evening, my wife is cooking I can hear the noise of utensils in the kitchen.
      • I stealthily enter the house and take out the bottle from my black cupboard.
      • Shivaji Maharaj is looking at me from the photo frame
      • But still no one is aware of it because I never take a risk
      • 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.
      • Of course I also keep the bottle inside my cupboard
      • Shivaji Maharaj is giving a smile  
      • I peep into the kitchen. My wife is cutting potatoes
      • But still no one is aware of what I did Becoz I never take a risk
      • I: Any news on Iyer's daughter's marriage
      • Wife: Nope, she doesn't seem to be that lucky. Still they are looking out for her
      • I again come out; there is a small noise of the black cupboard
      • But I don't make any sound while taking out the bottle
      • … contd
    • 31. I never take a risk (2of3)
      • … contd.
      • I take out the glass from the old rack above sink
      • Quickly enjoy one peg, Wash the bottle and keep it in the sink
      • Also keep the Black Glass in the cupboard
      • But still no one is aware of what I did
      • Becoz I never take a risk  
      • I: But still I think Iyer's daughter's age is not that much
      • Wife: What are you saying? She is 28 yrs old... like an aged horse
      • I:(I forgot her age is 28) Oh Oh...
      • I again take out potatoes out from my black cupboard
      • But the cupboard's place has automatically changed
      • I take out the bottle from the rack and quickly enjoy one peg in the sink
      • Shivaji Maharaj laughs loudly
      • 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
      • … contd.
    • 32. I never take a risk (3of3)
      • … contd.
      • 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...
      • 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
      • 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.
      • 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
      • Becoz Shivaji Maharaj never takes a risk
      • Iyer is still cooking. And I am looking at my wife from the photo and laughing…
    • 33. Interactive Session