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NOTES
Price=Coupon/(1+i)n+ FV/(1+i)n
• Coupon rate is NOT discount rate
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ANNUITY – Fixed amount, periodically and specified time period
PVA = CF* [ 1/r - 1/r(1+r)t]
2
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DISCOUNT RATE
PV = CF * Discounted flow
Discounted flow= 1/(1+r)t
Discount factor
DF = 1/(1+r)
BUILD IN FORMULA (EXCEL)
PV= (RATE, NUMBER OF PERIOD, PAYMENT, FACE VALUE, TYPE)
NET PRESENT VALUE

In case of annuity i
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periodic fixed amount cashflows
NPV= - INVESTMENT+ PVA OF INFLOWS
Worth of asset = CF [1/r – 1/r(1+r)t - time remaining

In case of different cashflows annually
NPV = - INVESTMENT + [CF1/(1+r)1 + CF2/ (1+r)2 + CFt/ (1+r)t]

Functions of Financial Market
Facilitate transfer of economic resources from lenders to ultimate borrowers
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Allow lenders to earn interest or dividend
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Facilitate credit creation
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Promote economic efficiency
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Financial Intermediaries
Financial intermediary is a financial institution that connects surplus and deficit agents
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• Depository Institutions
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• Contractual Savings Institutions
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o Casualty insurance companies
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• Investment intermediaries
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o Mutual funds
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BOND UNDERWRITING
Underwriting refers to the process where one or more banks or securities firms, forming a
syndicate, buy the entire issue of bonds from the issuer and re-sell them to investors
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• For smaller issues a private bond placement is common
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• An alternative process for bond issuance is on a “best efforts basis”, where no
underwriting takes place and the volume and price is determined by demand
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It usually takes place in the primary market
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•

STOCK Vs
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Whereas, Bondholders lend money to the company (by buying a part of company’s
debt)
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•

•
•
•

Bonds do not have a centralized place for trading, they are mainly sold over the counter
(OTC)
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e
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The stockholders are exposed to higher risks than the bondholders
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The bonds are susceptible to risk such as inflation and interest rate
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Bonds usually have a definite maturity period after which the bonds are redeemed
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Exception- irredeemable
bonds
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Credit ratings ARE opinions about relative credit risk
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• Ratings are not intended as guarantees of credit quality or as exact measures of the probability
that a particular issuer or debt issue will default
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Changes in credit rating, because•

Can be related to overall shifts:
– in the economy or
– business environment or
– specific industry or
– entity, or individual debt issue
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RA analyses the creditworthiness of a company which may lead to upgrade or downgrade in ratings
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• Portfolio of assets "pooled" and transferred => Special Purpose Vehicle (SPV)/the issuer
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• The issuer SPV issues securities to buy the assets from the originator
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Structured securitizationORIGINATOR(providers of loan) sells their loans to special purpose vehicles and the SPVs pay the
banks by the funds provided by the investors
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•
•
•
•

If originator(bank) goes bankrupt, the creditor (SPV) will not get the benefits of the assets
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e
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THE BONDS ARE BASICALLY PARTS OF ASSETS WHICH ARE SOLD TO THE INVESTORS
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THE AMOUNT IS TO BE
RETURNED BY THE SPV
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CREDIT STRUCTURING- Credit enhancement required for sufficient credit quality, ways to enhance– Internal credit enhancement
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• Overcollateralization (assets > notes)
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• Excess spread
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• Letter of credit, swap
Securitization REPAYMENT Structures•
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Static pool- No more mortgages allowed if the previous mortgage is still outstanding
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WATERFALL-

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The repayment is prioritized
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– I/P/I/P vs I/I/P/P, where I is
interest and P is principal on bonds
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Investors use the spread as in indication of the relative
pricing or valuation of a bond
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In a CDS, the buyer of the swap
makes payments (Like premium) to the swap's seller until the maturity date of a contract
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Probability of Default
•
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Cumulative – Overall likelihood of default (For all x years)
Marginal- Incremental probability of default (eg
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An investor can earn a return in 2 forms- stock price
appreciation and dividend
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DIFFERENCE•
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Stockholders have ownership stakes whereas bondholders have creditor stake
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STOCK VALUATION
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Dividend discounted models
Equity valuation multiple

CAPM is one of the models that can provide required rate of return, k
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If the sock is priced correctly, Actual return=expected return
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When,
IV > MV - Buy
IV < MV – Sell or short sell
IV=MV – Hold

Dividend Valuation MethodIt implies that the price of stock can be estimated using the dividend only
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Note- In case, a company incurs losses, PE ratio is not applicable
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Forms of EMH• The weak form (i
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random walk theory): prices reflect all the information in past prices (all
historical information)
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• The strong form: prices reflect all information (both public and private)
Random walk theory tracks day to day stock prices which does not show any pattern
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risky assets
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Slope of CAL is called reward-to-volatility ratio or Sharpe ratio
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e
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To calculate the portfolio • Return of 2 risky assets --- Return= W1* Return1 + W2* Return2
W1= weight of bond
W2=weight of equity

•

Portfolio Variance= 𝑤12 𝜎12 + 𝑤22 𝜎22 + 𝑤1 𝑤2 ⋅ cov(𝑟1 , 𝑟2 )

• Covariance of returns --- Cov(rD, rE ) = DEDE
DE= Correlation coefficient of returns

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Range of correlation coefficient = -1
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0
-1
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1
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•

Minimum Variance Portfolio
The Minimum Variance Portfolio is the portfolio composed of risky assets that has the
smallest standard deviation; the portfolio with least risk, for a given rate of return
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o More risk averse- invest more in risk free
o Less risk averse- invest more in risky assets
The optimal portfolio aims to include securities with the greatest potential returns given a
degree of risk or securities with the lowest degree of risk for a given level of potential
return
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Portfolios that lie below the efficient frontier are sub-optimal, as they do not offer enough
return for the level of risk
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e
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Monte Carlo Simulation- Assumptions are made about the mean, standard deviation
and correlation which helps in creating several hypothetical outcomes
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The simulated returns (%) are then used to calculate wealth values
($)
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LECTURE 7
Capital Asset Pricing modelReturn = rf + βi (rm- rf)
βi measures security’s i contribution of total risk of a well-diversified portfolio, namely the market
portfolio
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o Investors are compensated for holding systematic risk in the form of higher returns
o The magnitude of compensation depends on the equilibrium risk premium-- (rm- rf)

Single Index Model and realized returns
To move from expected to realized returns, use the index model in excess return form
𝐑 𝐢 = 𝛂 𝐢 + 𝛃𝐢 𝐑 𝐌 + 𝐞 𝐢
SECURITY CHARACTERISTIC LINE
➢ It is the regression line
➢ The Alpha stock can be desrcribed as 𝛼𝑖 = 𝐸(𝑅𝑖 ) − 𝑅𝑓 − 𝐵𝑖 [𝑅𝑚 − 𝑅𝑓 ]
Fama French Three-factor model
Two more factors are added, which includes➢ SMB= Small minus Big (Firm size)
➢ HML= High minus low ( book to market ratio)

R =i + im Rm + iSMB SMBt + iHML HMLt +ei
Arbitrage Pricing Theory
It is a one-period model in which every investor believes that the stochastic properties
of returns of capital assets are consistent with a factor structure
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o The ROR of market portfiolio plays no special role in APT
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Inconsistency in prices cause
arbitrage opportunity
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➢ Variables that influence returns are those that change the discount rate,
and the expected cash flows
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➢

In APT, the unanticipated components of factors are considered because the
knowns are already included in expected returns
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e
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Estimation of APT betas – slide 25
Empirical Evidence- slide 30
LECTURE 8
A derivative is a contract that derives its value from the performance of an underlying entity
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1) OPTION- This gives the investor a right, not an obligation, to buy or sell the underlying asset
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In Europe, it can only be
exercised on expiration date
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3) FUTURE- Like forwards but feature formalized and standardized contracts
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The futures
contract specifies the quantity and quality of the underlying asset and how it will be
delivered
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o For eg
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RIGHT-WAY RISK
When counterparty creditworthiness improves as its payment obligation increases
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LONG: A commitment to purchase the commodity on the delivery date
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Expect price at maturity will increase-

Profit long position = Spot price at maturity - Original futures price
Expect price at maturity will decrease-

Profit short position= Original futures price - Spot price at maturity
OPTIONS
Types•
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•
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Stock Options
Index Options
Futures Options
Foreign Currency Options
Interest Rate Options

CALL OPTION
A call option gives its holder the right to buy an asseto At strike price (decided price)

o It is useful when Market price > Strike price
PUT OPTION
o

A put option gives its holder the right to sell an asset:

– At the exercise/strike price
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o Exercise the option to sell the underlying asset if market value < strike price
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Sellers (writers) of options
receive premium income
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– Call: stock price - exercise price
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• Time value: the difference between the option price and the intrinsic value
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g
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It can be thought of as a measure of the probability of an option finishing in the money
on the maturity date
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Gamma is identical for put and call options
for European options
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A high gamma option requires
more frequent adjustments to remain effectively hedged
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𝜕𝑐
𝑉=
𝜕𝜎
THETA
Theta is the option’s sensitivity to a small change in time to maturity
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𝜕𝑝
𝑅ℎ𝑜 =
𝜕𝑟

CREDIT DERIVATIVES
Credit derivatives are offering payoffs based on changes in credit conditions
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Credit options can be tied to credit spreads
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The buyer makes periodic payments to the seller, and in return receives a payoff IF
an underlying financial instrument defaults or experiences a similar credit event

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