Efficient Market Hypothesis
Prices of securities reflect available information
Investors buying securities should expect to obtain an equilibrium rate of return
Active traders will find it difficult to outperform passive strategies
Macauly Duration Assumptions
Flat term structure
Single marginal shift to term structure that happens immediately
Parallel shift
Value weighted average time to maturity
Option Pricing in the multi-binomial model
Weaknesses of Mertons Firm Value Model
Cannot produce spreads for short time to maturity because sudden defaults in the model are impossible
Firms never default unexpectedly - prob. of default on short-term debt is zero
When is diversification beneficial
If assets are not perfectly correlated, then risk (measured by volatility) does not add up. It is thus beneficial to diversify.
Option Delta / Hedge Ratio
CDO’s
Collateralized debt obligations are used to reallocate the credit risk of a pool of loans.
The pool is sliced into tranches, with each tranche assigned a different level of seniority in terms of its claims on the cash flows from the underlying loans.
High seniority tranches are usually quite safe, with credit risk concentrated on the lower level tranches. Each tranche can be sold as a stand-alone security.
Hedging of interest rate risk
Duration and convexity can be used to quantify the interest rate exposure of a portfolio
This exposure can be controlled by using interest rate derivatives such as interest rate swaps or futures
Why must state prices be greater than zero
State prices must be greater than zero to avoid the possibility of arbitrage
Risk Neutral Probabilities
Risk-neutral probabilities are a mathematical construct that reflect the probability of an event occurring under the assumption that investors are risk-neutral.
Physical Probabilities
Physical probabilities are based on the actual likelihood of an event occurring in the real world. They take into account all the relevant factors that could affect the outcome of the event, such as historical data, market trends, and environmental factors. Physical probabilities reflect the actual risks and uncertainties inherent in the underlying assets or markets.
When is tranching most efficient
Tranching a portfolio consisting of bonds issued by a single firm
Tranching a portfolio of bonds issued by firms of the same industry
Tranching a portfolio of bonds issued by firms of different industries
By tranching a portfolio of high-yield bonds in a way that transfers virtually all default risk to junior tranches, it would still be possible for a senior tranche to carry a AAA rating
Firm Value Model Black Scholes
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