Financial Markets

CML

market expected return

beta

ARA

continuous return from discrete

duration

change in price using duration

convexity using discrete compounding

convexity using continuous compounding

hedge ratio

Pseudo probability, p

price of call option

min. number of ups to get positive payoff

RRA

= ARA*w

amount you would be willing to give up in a fair bet

market variance

covariance

put-call parity

call pricing using binomial approximation

Z₁

SD₁

P^I

upper bound for call option

upper bound for put option

lower bounds of call option

lower bounds for put options

two period binomial option pricing

three period binomial option pricing

risk neutral probabilities, q

forward prices, no income

forward prices, predictable income

forward prices, predictable yield

value of long forward

value of short forward

forward rate on currencies

forward rate on investment commodities

forward rate on consumption commodities

d₁

d₂

u =

d =

1/u

CAPM Assumptions

• no transaction costs

• all assets are infinitely divisible

• no personal taxes

• markets are purely competitive

• investors choose portfolios purely on expected return and standard deviation

• short sales permitted

• unlimited borrowing and lending at the risk free rate

• investors have homogenous expectations

arithmetic returns

• discrete compounding

• multiplicative cumulation

• non-symmetric reversal in return

• not normally distributed

logarithmic returns

• continuous compounding

• additive cumulation

• reversal in return is symmetric

• more normally distributed

fama French model

• extends CAPM to include two additional factors that capture systemic risk that is not explained by the market alone

• factors: market, size, value

• largely empirical

• explains more of the variation in average returns than CAPM

• empirically supported across many markets and long time periods

• lacks strong theoretical foundations

• interpretations of size and value factors still debated

carhart four factor model

• extends on mama French by adding momentum factor

• strong empirical support: captures size, value and momentum effects

• widely used in performance evaluation

• lacks deep theoretical foundation

• momentum may arise from behavioural biases rather than risk premia

CAPM vs APT

• CAPM is one factor only, APT has multiple factors

• CAPM has market risk only, several system risks priced in APT

• CAPM has weak empirical performance but APT has stronger

• core idea of CAPM = excess returns depend on exposure to market portfolio

• core idea of APT = expected returns are determined by multiple sources of systemic risk. condition of no arbitrage prevents mispricing.

effect of a decrease in market interest rate on utility of borrowers and lenders

• market interest rate = -(1+r)

• a fall in r makes the budget line flatter

• can now access a higher utility curve

• consumers consume more this period and next

effect of a decrease in market interest rate on the present wealth of borrowers and lenders

• pv of future income = income*1/1+r

• as r falls, pv of future income rises

• borrower has negative future net income, lower r reduces the pv of loan repayments, increasing the present wealth of borrowers

• lender has positive future income, lower r reduces pv of returns from lending - present wealth of lenders decreases

strategy for arbitrage

• buy the undervalued option

• short the stock if the option is a call

• buy the stock if the option is a put

• do this without borrowing - borrow cash if necessary

credit default swaps

• derivative contract that transfers credit risk of a borrower from one party to another

• protection buyer pays premium

• protection seller compensates buyer if credit event occurs

• settlement may be physical or cash

• mainly used to hedge credit risk, speculate on changes in credit quality, and improve pricing efficiency between bond and credit markets

• CDS involves counterparty risk, may encourage excessive speculation and can contribute to systemic risk if poorly regulated