risk concept and management 5

Author: Dilip ThosarFor IIIT Hinjewadi, PuneDecember 2007

Concept and Management of Risk Slide no. 1

April 10, 2023

Concept and Management of Risk



April 10, 2023

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%



April 10, 2023

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



April 10, 2023

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?



April 10, 2023

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 Rsecurity = Rf + m + ε– Rf is the riskfree return expectation– m is systematic risk premium– ε is unsystematic risk of security premium



April 10, 2023

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.

Type of Node Written Symbol Node Successor

Decision square ■ decision branches

Event circle ● event branches

Terminal endpoint ◄ terminal value



April 10, 2023

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.



April 10, 2023

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



April 10, 2023

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. Adobe Acrobat Document Microsoft Excel

Worksheet



April 10, 2023

The Decision Tree : Example



April 10, 2023

The Decision Tree : Example• Terminal Values, Rollback EVs, Choice

Indicators



April 10, 2023

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.



April 10, 2023

Sensitivity Analysis• Sensitivity (“what if” or “bop”)

– How does output vary with change in input

– Theoretically ∂ (Cashflow NPV) / ∂ factori

• Mechanism– List all factors Fi affecting output NPV

– List Optimistic, Realistic and Pessimistic values for each factor Fi

– Evaluate Output (NPV) for each possibility– Inspect the resultant table for sensitivity



April 10, 2023

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) * A5,15% - 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



April 10, 2023

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 + A5,15% * 90 = 1517



April 10, 2023

Sensitivity Analysis : Example• BOP values for factors and NPV sensitivity



April 10, 2023

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



April 10, 2023

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.



April 10, 2023

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)



April 10, 2023

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.



April 10, 2023

Normal Distribution



April 10, 2023

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



April 10, 2023

CAPM: Capital Asset Pricing Model• E(Ri) = Rf + βim * (E(Rm) – Rf)Where• E(Ri) is the expected return on the capital asset • Rf 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

• Rm is the expected return on the market portfolio• βim , “beta coefficient” is the sensitivity of the asset

returns to market returns (Rmarket – Rriskfree) 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)



April 10, 2023

CAPM



April 10, 2023

The Beta in CAPM• βim = Cov (Ri, Rm)/Var(Rf), where

– Ri is the expected return on the capital asset– Rm 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



April 10, 2023

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



April 10, 2023

Capital Gains• Rise of value of Capital Investment• Capital Gain = (Pt+1 – Pt). %Capital Gain = (Pt+1 – Pt) /Pt

• 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



April 10, 2023

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



April 10, 2023

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



April 10, 2023

The lighter side: I never take a riskWhen 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 frameBut 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 potatoesBut 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 cupboardBut I don't make any sound while taking out the bottle

…contd



April 10, 2023

I never take a risk (2of3)…contd.

I take out the glass from the old rack above sinkQuickly enjoy one peg, Wash the bottle and keep it in the sink Also keep the Black Glass in the cupboardBut 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 muchWife: 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 changedI 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 cupboardWife is keeping the sink on the stoveBut still no one is aware of what I did Becoz I never take a risk

…contd.



April 10, 2023

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 potatoesGo in the black cupboard and enjoy a peg Wash the sink and keep it over the rackWife is giving a smileShivaji Maharaj is still cookingBut still no one is aware of what I didBecoz 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 didBecoz Shivaji Maharaj never takes a risk

Iyer is still cooking. And I am looking at my wife from the photo and laughing…



April 10, 2023

Interactive Session

risk concept and management 5

Technology

decision outcome

outcome decision

concept of risk risk

branch value

event node probability

decision tree

terminal node value

rollback value value