Basic Principles of Investor Behavior, Valuation, Risk and Derivatives

Pair of Concurrent Decisions

Decision 1

A: Sure gain of 2,40,000

B: 25% chance of 10,00,000 and 75% chance of 0

Decision 2

C: Sure loss of 7,50,000

D: 25% chance of losing 0 and 75% chance of losing 10,00,000

Concurrent DecisionsDecision 1A: Sure gain of 2,40,000B: 25% chance of 10,00,000 and 75% chance of 0Decision 2C: Sure loss of 7,50,000D: 25% chance of losing 0 and 75% chance of losing 10,00,000

Behavior PatternsB and C and A and C is equivalent to risk averse behaviorB and D is equivalent to risk-seeking behaviorA and D is equivalent to irrational behavior

Basic Concepts Test

Q1. Which of the following does not cause accounting financial statements to differ from economic reality?A. Rigidity of accounting rules

B. Random forecast errors

C. Management discretion

D. Debt covenants

Q2. Which of these is not a cause of concern to an analyst while doing accounting analysis of a company?A. Unexplained changes in accounting policy

B. Unexplained profit boosting transactions

C. Low sales growth

D. Larger bad debt provisions in years of high profit

Q3. Buyer of a Straddle benefits when:A. Stock price moves up but not down

B. Stock price moves down but not up

C. Stock price moves within a small range

D. Stock price moves either up or down as long as it moves significantly

Q4. Which of these is not a specific risk from an investments perspective?A. Financial Risk

B. Interest Rate Risk

C. Credit Risk

D. Liquidity Risk

Q5. Which of the following actions is NOT considered Earnings Management?A. Changes in Revenue recognition policy

B. Changes in Depreciation Policy

C. Booking inventory at lower of historical cost and market valueD. Writing off bad assets in high profit years

Q6. What is Moral hazard?A. Expected loss to individuals due to ethical behaviourB. Expected loss to shareholders from managers trying to gain private benefits post the contractC. Expected loss to principal from agent not revealing the information prior to writing a contract

D. None of these

Q7. Which of the following statements is NOT correct?The risk reduction is high for the first few stocks added to a portfolio but with each additional stock, the risk reduction is lesser

B. Risk can be reduced to zero with complete diversificationC. Risk can be reduced further if we diversify across asset classes and across geographies

D. As investors add stocks to a portfolio, their risk reduces due to diversification

Q8. What does Treynor ratio signify?A. The excess return over expected return from CAPM

B. The excess return over the risk free rate compared to total risk of the portfolio

C. The excess return over the risk-free rate compared to undiversifiable risk of the portfolio

D. The excess return over the market return

Q9. Which of these forms of efficient market hypothesis was violated in the Rajat Gupta scam?A. Weak form of Efficient Market Hypothesis

B. Semi-strong form of Efficient Market Hypothesis

C. Strong form of Efficient Market Hypothesis

D. All of these

Q10. A credit default swap (CDS) is what kind of a product?A. A put option on the underlying loan

B. A call option on the underlying loan

C. A forward contract on the underlying loan

D. A futures contract on an underlying loan

Answer Key

DCDACBBCC10. A

Let us suppose that there are two stocks in the market (A and B) which are trading at the following pricesPrice of A = INR 50Price of B = INR 38If we assume that price of A can either go to 75 in a good economy (B will rise to 60) or to 40 in a poor economy (B will fall to 32), is there an arbitrage opportunity if the risk-free rate is 4%?Basic Arbitrage pricing mechanism

Suppose that a stock A is selling for 50 in the market and its one-year future is selling for 54. Is there an arbitrage opportunity if the risk-free rate in 6%?A realistic arbitrage pricing example

Then what do arbitrageurs do?The existence of arbitrage opportunities ensures that there are arbitrageurs n the marketThe existence of arbitrageurs ensures that the arbitrage opportunities do not last for longIf no arbitrage exists..

Introduction to Valuation

Why value companies ?Price is what you payValue is what you getThe basic purpose of valuation is to find the right price to be paid/receivedThe purpose is not just to evaluate the value of an asset but also the source of this value

Why value companies ?Every asset has a valueAlthough the techniques may differ but the basic principles remain the sameCommon sense says that you should not pay more for an asset than it is worthBut Bigger fool theory prevails

Role of valuationFundamental analystsThe investment rationale is valuationTechnical analystsTo develop support and resistance levelsInformation tradersFor the relationship between information and valueMarket timersEvaluating whether market is under-valued or over-valuedEfficient marketersTo find out the implicit assumptions of growth and risk in the market

Role of valuation AcquisitionsValue from acquirers perspectiveValue from targets perspectiveValue of synergyValue of changing managementValue of restructuring

Concept CheckerValue of an asset depends on the demand and supply in the marketValue is determined by investor perceptions about the assetValue of an asset depends on the methodology or the model usedValue of an asset will depend upon the assumptions used in a model

Introduction to risk

Why is risk important?The returns from any asset have to be measured after adjusting for their riskWe do this in a DCF method of valuation through the discount rates we use to arrive at present value of future cash flowsCost of debt has to include the possibility of defaultCost of equity has to include the equity risk premium

Equity RiskThe risk for any equity is measured by its estimated variance (or standard deviation) around its estimated returnHowever, we do not consider variance as the appropriate measure of risk while valuing securitiesThis is because we can reduce some part of this risk through diversificationThe diversifiable amount of risk is known as the unsystematic risk

Equity Risk continuedThe undiversifiable part of risk known as systematic risk or market risk is measured by the sensitivity of the firms return to market returnsThere are four common ways to estimate a stocks riskCAPM modelAPT modelsMultifactor modelsRegression models

Why only market risk?The diversifiable part of the risk is not important because a rational investor will not really be demanding any excess return for this risk since he knows that it can be diversified awayHow risk can be diversifiedBy adding more stocks to a portfolio, any one stock forms a smaller percentage of the whole portfolioThe excess losses in one stock tend to be cancelled out to some extent by excess returns in some other stock making the average deviation of the portfolio lesser

Cost of Equity CAPM ModelIn CAPM, we use to define the sensitivity of firms returns to market returnsThe expected return on any stock is then defined as:-ke = Rf + * (Rm Rf)

Cost of Equity APT ModelThis model is based on the Law of One price and assumes that arbitrageurs are continuously at work to not allow arbitrage opportunities for extended lengths of timeke = Rf + 1 * [Rm Rf] + 2 * [Rm Rf] + + n * [Rm Rf]The factors are not known beforehand but are derived statistically

Cost of Equity Multi-factor ModelThe multi-factor model is a variation of an APT model where we replace the unknown factors with known economic variablesThe ke = Rf + GNP * [RGNP Rf] + I * [RI Rf]The factors are estimated by us and then we use historical statistical analysis to arrive at the beta values

Cost of Equity Regression ModelThe multi-factor model is a variation of an APT model where we replace the unknown factors with known economic variablesThe ke = Rf + a * Ra + b * Rb + ..+ n * Rn The factors are estimated by us and then we use historical statistical analysis to arrive at the beta values

Measuring equity risk Risk Free Rate

Risk-free RateNormally, we first identify a risk-free asset and take the returns promised by such an asset to be risk-freeBut how do we define a risk-free asset?And what is to be done when such an asset is not available?

Risk-free assetA risk-free asset is one where the expected return is equal to the realized return. This means thatThere is no default riskThere is no reinvestment riskThis means that the asset under consideration must have the same time horizon as our investment horizon and there should be no coupons that need to be reinvested

Risk-free assetThis however, implies that for different years of expected returns, we should have different risk-free ratesHowever, the losses from using a common risk-free rate by duration matching methodology are not huge as long as the term structure is not steep

Risk-free rateThe risk-free rate has to be consistent not with the country of the project but with the currency in which the cash flows are projectedFor a company having operations in different countries, we can value its business in different currencies. We might believe that the differences in risk-free rates of currencies could cause differences in valuation, but the purchasing power parity concept ensures that in the long-term the values will converge

Nominal and real risk-free ratesWhen inflation is very high, the valuation exercise has to be done in real terms rather than nominal termsThis implies that both the risk-free rate and the growth rate have to be taken after removing the returns and growth coming from inflationThe real risk-free rate under such circumstances is taken to be equal to the real sustainable growth rate of the economy

Measuring equity risk Risk Premium

Equity risk premiumEveryone agrees to the concept that for investing in assets that have higher risk, investors require higher returnsThe disagreement lies in the methodology used to measure this higher risk and to convert this higher risk measure to a required return which would compensate for this higher risk

Equity risk premium . continuedTo measure the equity risk premium, we need to measure two things:-What do investors on average require as a premium over the risk-free rate for an investment with average risk (Risk Premium)What is the additional risk that a new investment adds to a well diversified portfolio (Beta)

Historical risk premium approachThe actual returns on a market portfolio are compared to risk-free rates on a default-free asset. The average difference, on an annualized basis, is estimated as the risk premiumThere are however a few things which may change our estimatesTime period usedMore updated premium Vs estimation errorChoice of risk-free rateConsistency between the risk-free rate and the risk premiumArithmetic Vs geometric averages

Historical risk premium approach - CaveatsAssumption is that investor return requirements for risks have not changed over timeA shorter time period creates more estimation errorA longer time period fails to capture the effect of changing investor expectationsSurvivorship bias

Risk premium for markets with lesser historyFor markets which do not have enough reliable data, the estimation errors would be too huge. For such markets, we can sayRisk Premium = Risk premium for mature markets + Country risk premiumWhat should be the risk premium for mature markets?How do we estimate the country risk premium?

Risk premium for markets with lesser historyWhat should be the risk premium for mature markets?Take returns on any market with a long (20-30 years at least) history of stocks returns and little or no political risksHow do we estimate the country risk premium?Use default spreadsAlthough these have lag effects, synthetic ratings are an alternativeUse relative standard deviationsLow liquidity may understate the risk premiums in some marketsStandard deviations must be measured in a common currency

Risk premium for markets with lesser historyHow do we estimate the country risk premium?Use default spreads + relative standard deviationsThe default spreads measure only the risk of defaultHowever, that is not the only riskThus we can calculate the country risk premium in the following wayCountry risk premium = Default spread * Relative standard deviationThe difference between this approach and the previous one is that the previous approach uses the mature country equity standard deviation as a base while this approach uses the same countrys bond standard deviation

Asset exposures to country risk premiumHow do we add the country risk premiums once we have measured them?Assume all companies have the same exposure and add the country risk premiums to all companiesAssume that a companys exposure to country risk is same as its exposure to all other market risk (measured by beta)Assume that there is a separate sensitivity to country risk as compared to its sensitivity towards other market risk

Estimating default spreadsWe first take a sample of bonds with the similar rating as the rating class whose spread we are trying to measureNext we estimate the YTM on each of these bondsTake an averageUse weighted average weighted by trading volumeDecide a benchmark using similar maturity

Measuring equity risk Beta

Historical market betaBeta measures the sensitivity of a firms expected return to the expected return on the marketWe can estimate a firms beta by regressing its stocks returns against the market portfolio (use a market index as a proxy)Statistically speaking beta is defined as Beta () = im * i /m

Historical market betaA regression estimate of beta gives four important characteristicsThe slope of the regression which defines the beta of the stockThe intercept which when compared to Rf *(1 - ) defines the excess return over expected returnThe R-square defines the percentage of variation explained by market riskThe standard error of beta estimate can be used to estimate the interval over which the true value of beta will lie with a certain degree of confidence

Historical market betaThere are three considerations in historical estimation of betaLength of estimation periodThe fundamentals of either the company or the market should not have changed significantlyReturn intervalHigher return intervals remove the downward bias due to illiquidityChoice of market indexIndex should not be dominated by a few companiesApart from this there is some merit in using adjusted betas for firms

Fundamental betaThe beta of any firm depends on three thingsThe business the firm is inThe operating leverage of the firmThis implies that smaller firms or firms with higher growth will have higher betaThe financial leverage of the firmL = U * (1 + (1 t) * (D/E))The unlevered beta (or asset beta) measures the riskiness inherent due to the type of business and operating leverage in the firm. The levered or equity beta also includes the effect of financing choices

Fundamental beta Bottom up betaThe asset beta of two assets put together is a weighted average of their asset betas with the weights being dependent on market valueSteps in calculating bottom up betaIdentify business or businesses a firm operates inIdentify peers in each business line, their regression betas and their financial leveragesEstimate average unlevered beta for the peersEstimate unlevered beta for the firm under analysis, by taking weighted average of unlevered betas across its business lines with the weights being market values of capital in the businessesEstimate current market values of debt and equity and lever the unlevered beta by the firms debt-equity ratio

Fundamental beta Bottom up betaThe bottom-up beta gives a better estimate of betaAverage across different regression beta would have lower standard errorsA bottom up beta can easily reflect changes in business mix of a firmEffects of changing debt equity ratio can be incorporated

Fundamental beta Bottom up betaWe have to consider many things while arriving at a bottom up betaDefinition of comparable firms (Defining the business you are in)Estimating betasUsing service betas against calculating betas yourselfAveraging methodSimple average Vs weighted averageControlling for differences

Accounting BetaThe third approach to beta is to measure the change in a firms earning compared to changes the earnings for the whole marketThe method has three pitfallsAccounting earnings are smoothed out causing the betas to be biased towards oneAccounting earnings can be influenced by non-operating factorsThere are too few data points

Measuring debt risk

Measuring cost of debtThe cost of debt measures the current cost to raise debt for a firmIt is not equal to the historical interest rate divided by the average debt of the firmIt has the following variablesThe risk-free rateThe default riskTax advantage associated with the debtWhich tax rate to take?

Measuring cost of debtCost of debt can be used by any of the following methodsIf a company has long term bonds which are actively traded in the market, the YTM on such bonds can be treated as the cost of debtIf the company has been rated recently, its rating and average risk premium over that rating can be usedIf the company has issued any debt recently and the companies fundamentals have not changed, the cost of debt recently issued can be taken as the cost of debt going forwardIf all the above are not available, then synthetic rating or regression models are the most suitable

Measuring risk of hybrid securities

Measuring cost of other hybrid securitiesCost of preferred capitalThis can be estimated as the preferred dividend per share divided by the market price per preferred shareCost of convertible securitiesThe price of the convertible securities should be separated by value into debt and equityAfter that the individual costs of debt and equity should be used to estimate cost of the security

Measuring WACC

WACCThe weights to be used in WACC estimation should be market values of debt and equityWeight for debtWe should consider only interest bearing liabilities. We should include both short-term and long-term debtWe should capitalize operating leases and use the value of the debt created for the weightWACC = ke * we + kd (post tax) * wd + kpf * wpf

Forward contracts

Forward contractsIn a forward contract the party making the commitment to purchase the underlying is said to have a long position and the other party is said to have short position

Forward contracts continuedNormally the forward contracts are designed to be held till maturityHowever, the long or the short have the option of terminating the contract before maturity by entering into an offsetting transactionThe offsetting transaction though would most probably have a different price causing the offsetting party to book a gain or loss on the transactionThe party entering into an offsetting contract still has credit exposure to both contracts unless the offsetting transaction and the original transaction have the same counter-party

Forward contracts Market StructureThe forward markets have many financial institutions which make markets or deal in the forward contractsDealers deal with either end-users or other partiesEnd-users normally have a risk-management problem while other parties normally have speculative interestsThe dealers are normally ready to take any side on a particular transaction having different prices for eachThe bid-ask mechanism

Forward contracts Market StructureWhy would the dealers be ready to take any side of a position?Because dealers believe that they can get into an offsetting transaction at a different price and thereby earn the spread between the two pricesIn that sense dealers are wholesalers of risk in the market

Equity ForwardsForward contracts on individual stocksForward contracts on stock portfoliosForward contracts on stock indices

Bond forwardsForward contracts on individual bondsDefault riskExpiryIf a 180 day T-bill is trading at a 4% discount what the price of the contract for no arbitrage (Assume 360 day convention)

Forward rate agreementsThese are essentially forward contracts on interest ratesThey are based on a underlying rate such as LIBORIf a London Bank needs to borrow USD 10 mn for 30 days and the 30-day LIBOR is 5%, calculate the amount it will owe in 30 days

Forward rate agreementsSuppose that Bank A wishes to take a 180 day loan 90 days from now. The bank does not want to bear the risk of 180-day LIBOR increasing in the next 90 days. Thus, it locks in a forward rate of 5% bu buying a forward rate agreement on a notional amount of USD 10 mn. The 180-day LIBOR then increases to 6% in 90 days. What is the pay-off to/from the bank after 90 days?

Forward rate agreementsPayoff to the long party is defined as[ Notional Principal * (Underlying rate at expiration Forward contract rate) * (Days in underlying rate/360)] / [ 1+ (Underlying rate at expiration) *( Days in underlying rate/360)]

Currency forwardsIn a currency forward contract one-party (the long) decides to buy a particular currency at a predefined exchange rate in some other currency at a future date with a notional principalSuppose Microsoft will receive Euro 12 mn in six months and does not want the exchange rate risk. Thus Microsoft will go short on Euro in a currency forward and long on dollars with a notional principal of Euro 12 mn. Suppose that the forward rate is USD 0.925 and the spot rate after six months is USD 0.920, what is the payoff to/from Microsoft after six months?

Other types of forward contractsCommodity forwardsWeather derivatives

Futures contracts

Futures contractsThe futures contract is similar to a forward contract except that it is standardized and traded on an exchangeWhen a buyer and a seller make a transaction, it is in effect recorded as the buyer making a transaction with the exchange and the seller making a transaction with the exchange

Futures contractsUnlike forwards, the exchange decides on all the important characteristics of a futures contract except its priceThus the exchange decides the underlying, the expiration date, the quantity per contract, the quality of the underlying, the tick size, the delivery mechanism and the place of delivery (in case it is not cash settlement)

Futures contractsThe homogenization of futures contracts increase liquidity and help in easy offsetting transactionsA person takes a position (either long or short) in the futures and incurs losses or makes profits of his position on a daily basisThe person may at a later date prior to expiration enter into an opposite transaction thereby booking whatever profits or losses he has made in the interim

Futures contracts The ClearinghouseThe margin in a futures market is different from the margin in a stock marketBoth the buyer and the seller in a futures contract deposit some amount in the begining of the contract with the clearinghouse as a collateral. This amount is called the initial margin requirement and is usually calculated as a percentage of the futures priceThe margin requirement in a futures contract is generally set by the clearinghouse and not the regulatory authority

Futures contracts The ClearinghouseThe clearinghouse also determines a maintenance margin requirement and then monitors the accounts on a daily basisThe daily amount of profit (loss) is credited to (debited from) the margin accountIf the money, in the margin account falls below the maintenance margin, then either the trader must close out the position and pay whatever dues are there or else bring the margin back up to the initial margin requirementTo calculate the daily changes, the clearinghouse determines a settlement price for the day (average of the last few trades)

Futures contracts The ClearinghouseAssume that a trader establishes a position in 10 contracts at a futures price of Rs 100. Assume that the settlement price for the day is also 100. The initial margin requirement is Rs. 5 per contract, the maintenance margin requirement is Rs 3 per contract. Calculate the amount of money deposited on each day and the amount of money at the end of each day for both a long and a short position if the following price changes occurDay 0 price is 100, Day 1 price is 99.2, Day 2 price is 96, Day 3 price is 101, Day 4 price is 103.5, Day 5 price is 103 and Day 6 price is 104

Futures contracts The ClearinghouseLimit movesExchange reserves the right to mark contracts to market even during a trading day

Treasury Bill FuturesA treasury bill future trades at a discount to the face value of the futures contractThe price of a futures contract on any day is 100 (Quoted rate) *( Days to expiry/360)Dollar value of basis point

Other futuresFutures on bondsConversion factorCheapest to deliver bondStock Index futuresCurrency futures contracts

Options

OptionsA call (put) option gives the right to the buyer to buy (sell) the underlying at a pre-specified price to the seller on or before the expiration dateThe option buyer is known as the long position holder and the option seller is known as the short position holderThe up front money paid by the option buyer is known as the option price or the option premium

OptionsOptions are both over-the-counter (OTC) and exchange listedExchange listed options have all their terms decided by the exchange except for the price which is determined by the marketOTC options have all their terms decided upon between the two partiesThe default risk lies with the option buyer/exchange

OptionsPrice of an option depends on the time to expiry, the volatility in the underlying, the interest rates in the market and the exercise price (with respect to the current underlying price)Call options have lower premium for higher exercise price while put options have lower premium for lower exercise priceBoth options are cheaper with less time to expiry

Types of OptionsStock optionsIndex optionsBond optionsInterest rate optionsIn interest rate call, the holder has the right to make fixed payment and receive floating and vice versaInterest rate caps / floors / collarsCurrency options

Option payoffsPayoff diagramsLong call optionShort call optionLong put optionShort put optionIntrinsic valueTime Value

Option minimum and maximum valuesMinimum value of any option is zeroMaximum value for call options is equal to the underlying priceMaximum value for the put option depends on whether it is an American option or a European optionMax Value of American put = XMax value of European put = X/(1 + r)T

Put Call ParityA fiduciary call has a European call option and a risk-free bondA protective put has the underlying and the European put optionSynthetic call/synthetic puts

An arbitrage opportunity using optionsCall options with an exercise price of 100 and time to expiry = 6 months is priced at 7.5Risk-free rate = 10%Put option with the exercise price of 100 is priced at 4.25The underlying price is 99State if there is an arbitrage opportunity and if so, then how it can be used to generate risk-less profits

Effects of interest rates and volatilityWhen volatility is higher, the prices of all options are higherWhen interest rates are high, the prices of call options are high and put options are low

Greeks in optionsDelta is the sensitivity of the option price to a change in the underlying priceGamma is the sensitivity of delta to a change in the underlying priceRho is the sensitivity of the option price to the risk-free rateTheta is the rate at which time value of an option decays with timeVega is the sensitivity of the option price to volatility

Discrete-time option pricing modelOne period modelC+ = Max(0, S+ - X)C- = Max(0,S- - X)U = S+/SD = S-/SNow let us buy n units of the underlying and sell 1 call option

Discrete-time option pricing modelThis means that our portfolio value will beH = nS cOne period later, the portfolio value is either of the two valuesH+ = nS+ - c+H- = nS- - c-Let us choose a value of n for which H+ = H-This will give us the value for n asN = (c+ - c- )/ (S+ - S- )

Discrete-time option pricing modelA completely hedged portfolio should grow at the risk-free rateThus H+ = H- = H * (1 + r)Solving the equations we get, c = [ * c+ + (1 ) * c- ]/ (1 + r) where = ( 1+ r d)/ (u d)

One period option exampleLet the underlying price of a stock be 50The stock can either go up by 25% or go down by 20%Find the value of a call option with the exercise price of 50 and the risk-free rate of 7%Show the existence of an arbitrage opportunity if the call option is trading for Rs. 8

Thank You