Asset Markets (2nd half)

Question 1

Factor-replicating portfolio (*EXAMPLE)

Answer 1

• asset A with factor loadings b(A,1) & b(A,2)
• we are going to form a portfolio of the factor replicating portfolios and the risk-free asset which has identical factor loadings to A.
• by absence of arbitrage (and identical loadings and no specific risk)

Question 2

Differences/advantages/disadvantages of CAPM vs APT

Answer 2

CAPM: equilibrium model built on its foundation of mean-variance analysis.
APT: base on assumed factor structure along with an application of arbitrage. + is the pricing equation for well-diversified portfolios (i.e. mutual funds)
- via absence of arbitrage, it should be (approx.) valid for any large subset of risky assets*, whereas CAPM requires us to know the composition of the market portfolio.
- need to identify the APT factors; applications include portfolio selection and performance evaluation.
- *APT greatly simplifies the covariance matrix of security returns.

Question 3

Definition of abnormal returns

Answer 3

A market is efficient if price deviations from equilibrium are not predictable.

Question 4

Weak, semi-strong and strong form definition

Answer 4

Weak: if we cannot earn abnormal returns by using information contained in past prices (renders TA futile)
Semi-strong: if we cannot earn abnormal returns by using publicly available information.
Strong: if we cannot earn abnormal return by using all publicly and privately available information.

Question 5

Statistical tests of market efficiency

Answer 5

Weak: serial correlation (…)
Semi-strong: price reactions to company announcements (consider CAR, over/underreaction…, evidence on PEAD is not fully favourable to semi-strong) & performance of mutual funds
Strong: trades of company insiders

Question 6

Sharpe ratio

Answer 6

• reward-to-variability ratio for a portfolio = slope of CML
• tells us how well the portfolio performed relative to an efficient portfolio with the same total variance
  => may not be appropriate to use as a measure for funds that are part of a larger portfolio* - we ought to look at measures that consider return relative to the systematic risk of the portfolio.

Question 7

Jensen’s alpha

Answer 7

• the return achieved in excess of expected return for given beta (based on CAPM). N.B. APT-based alpha will contain more factors

Question 8

Treynor measure

Answer 8

• uses systematic risk instead of total risk (like the Sharpe Ratio)

Question 9

Appraisal ratio

Answer 9

• JA & TM are not adjusted for the amount of idiosyncratic risk in the fund/portfolio -> the less idiosyncratic risk, the more of the fund we can add to a diversified portfolio without driving up the total variance too much. (note formula)
• measures the cost-benefit ratio of an actively-managed fund providing positive alpha -> how much return the manager brings per unit of unsystematic risk

Question 10

Information Ratio

Answer 10

• uses the benchmark adjusted returns rather than regression residuals in the calculation of the mean & variance.

Question 11

M^2

Answer 11

Uses a benchmark to express performance differentials.

• give the absolute number context as opposed to SR
• gives adjusted (for risk) annual excess return over benchmark

Question 12

Market anomaly definition + possible explanations + example?

Answer 12

Investment strategies that seem to earn high returns without being very risky.

• strategy is simply risky
• ignoring transaction cots
• data mining
• risk might be measured incorrectly.

January effect: may be explained by; small firm effect, tax-loss selling, infusion of capital at the beginning of the year (investors sell winners to incur year-end capital gains taxes in December and use those funds to speculate on weaker performers.

Question 13

How to exploit a market anomaly?

Answer 13

Contrarian strategy: buy a portfolio of stocks that a have underperformed; sell stocks that have outperformed over the same period
OR
Zero-cost portfolio that buys winners and sells loser from the passt 6 months earns an average annualised return of approx. 12%.

(nb. mean reversion comes over a longer horizon than momentum strategies)

Question 14

Behavioural sources of market inefficiencies

Answer 14

• overconfidence (largely based on gender)
• confirmation biases
• anchoring
• disposition effect (sell winners too quick and vice versa)
• prospect theory
• loss aversion

Question 15

Forward definition

Answer 15

Obligation to buy/sell underlying asset at a particular time & price.

Question 16

Future definition

Answer 16

Obligation to buy/sell underlying asset at a particular time & price. Typically standardized* and traded on an exchange + gains and losses are settled daily.

Question 17

Uses of forwards and futures

Answer 17

• hedging
• speculation
• funding e.g. repo

Question 18

Payoff diagram for a forward

Answer 18

• LONG: upward sloping S(t) - F payoff

- SELL: downward sloping F - S(t)

Question 19

Future contract payoffs from selling & holding

Answer 19

• BUYING then SELLING: F(t) - F(t-1)

- HOLDING until maturity: S(t) - F(T-1)

Question 20

Constructing a hedged porfolio (buy stock, sell futures & resultant portfolio)

Answer 20

• how many shares you own
• sell y futures contract (N.B. contract size)
• identify value of y for which S(t) is equal to zero.
• > can then calculate hedged portfolio price

Question 21

*Exploiting a riskless arbitrage if the forward price deviates from spot-futures relation

Answer 21

Create table with: sell forward, buy stock, borrow (& net)

• forward contract will always be worth zero NOW
• if selling the forward, BORROW discounted F
• *if you long forward??

Question 22

Replicating portfolio of forward contract

Answer 22

Cash flows in 2x2 table: Now vs Maturity. Forward vs. Replicating

Question 23

Commodity futures (formulas)

Answer 23

• upward sloping forward curve if the risk-free rate is greater than the dividend yield
• downward sloping forward curve vice versa
• storage costs (costs of carry)
• convenience yield: commodities offer the “intangible” benefits of holding the underlying spot for those who consume it/use it in production (therefore arbitrage strategies do not work well for commodities)
• CY = spot - forward + interest cost + storage cost
• note: convenience yields are strongly positively correlated with demand relative to inventory of the commodity

Question 24

CIP intuition

Answer 24

• investors have an incentive to borrow in low-interest countries and save in high-interest countries.
• always the risk that high-interest currency could depreciate
• if you want to avoid this risk by locking in the future exchange rate (…back to domestic currency), the forward exchange rate must exactly offset any benefit from the higher interest rate
• eliminates the arbitrage oppotunity

Question 25

CIP intuition (+UIP difference)

Answer 25

- investors have an incentive to borrow in low-interest countries and save in high-interest countries. - always the risk that high-interest currency could depreciate - if you want to avoid this risk by locking in the future exchange rate (...back to domestic currency), the forward exchange rate must exactly offset any benefit from the higher interest rate - eliminates the arbitrage opportunity - UIP uses the expected spot rate rather than the forward

Question 26

Interest rate swaps

Answer 26

- agreement between parties to exchange cash flows in the future. - exchange fixed interest rate (k) for a floating interests rate at some notional principle, N. - K can be determined from the condition that the value of the Floating Rate Note (FRN) equals the value of a coupon bond with coupon rate k.

Question 27

Put & call payoffs

Answer 27

Call: ( S(t) - K )^+ Putt: ( K - S(t) )^+

Question 28

Uses of options

Answer 28

1) Speculation (allows you to leverage) => inherently much riskier 2) Hedging

Question 29

Straddle

Answer 29

Involves buying both a put and a call option with the same maturity and at the same strike price. - Profit when the price of the security rises or falls by an amount more than the total cost of the premiums paid.

Question 30

Reverse Straddle

Answer 30

Involves selling a call and a put | - the maximum profit is the premiums obtained from selling the securities.

Question 31

Bull Spread

Answer 31

Buy a call and sell a call with a higher strike price (can be for a put?). - profit from a moderate rise in the price of an underlying asset

Question 32

Bear Spread

Answer 32

Buy a put and sell a put with a lower strike price. | - profit from a (moderate) decline in the price of the underlying asset price.

Question 33

Butterfly spread*

Answer 33

Involves four options at three different strike prices. Combines a bull and bear spread. - profit if the underlying asset does not move

Question 34

How to exploit an arbitrage where put-call parity does not hold

Answer 34

- call, put, stock, bond - now & maturity ( S(t)k) - always sell the option (call or put) that is OVERpriced

Question 35

Binomial model

Answer 35

- generalised replicating portfolio using delta (shares) and B (bonds) - generalised option pricing formula (for a call - what about a put?) N.B. 'delta of an option' - a long position in the call is perfectly hedged (...pays off the bond) by selling delta shares of the stock -> the call is replicated by a leveraged position in the stock.* REPLICATION: determine replicating portfolio & then price of the RP (equal to price of the option) RNP: determine the RNP (q) (N.B. formula for q). Price of the option is the PV of expected cash flows, discounted at the riskless rate.

Question 36

American option

Answer 36

- need to work backward from final period. At each node, we must check whether early exercise is optimal, depending on stock price. - N.B. it is never optimal to exercise early an American call on a non-dividend paying stock. Therefore, price for non-dividend paying stocks will be identical to the European option.

Question 37

Exotic options

Answer 37

Path dependent options: - lookback call: option to buy the underlying asset at the min price which it reaches during the life of the option. - average strike Asian call: the option to buy the underlying asset at the average price of the asset during the life of the option. - average price Asian call * non-recombining tree. * **defaultable bond example??!!