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Duration of equity in leveraged portfolio
 Basically
 De = duration of equity
 Db = duration of borrowed
 Dp = duration of portfolio

Description; drawbacks of following bond measures of risk
1. variance/std dev
2. semivariance
3. shortfall risk
4. value at risk
 1. dispersion around mean; returns are nonnormal, requires n(n+1)/2 inputs, inputs constantly changing
 2. dispersion results below target return; same as above, and less accurate b/c uses half of the data
 3. probability that actual return is less than target return; provides probability only, not what level of losses could be below target
 4. estimated loss over specified time period at specified probability; does not quantify what happens to return at less than the specified probability  ex. 50% chance lose 5%, but may be a 30% chance lose 90% that is not communicated

Compute number of futures contracts needed for desired portfolio duration
 Dt = target duration
 Dp = current duration
 Vp = value of portfolio
 Dctd = duration of cheapest to deliver
 Pctd = price of cheapest to deliver
 CF = ctd conversion factor
 Yield Beta = ratio of yield changes for item being hedged and CTD; yield beta is 1 unless told otherwise

Calculate duration of a swap
 Dasset  Dliab, so Dreceive  Dpay
 Drec = reset period (in years) / 2; usually .5/2 = .25
 Dpay = .75*(swap length in years)

Calculate the duration of an option
Dopt = Delta of option * Duration underlying * (Price underlying/Price option)

Three types of credit risk
 default risk
 downgrade risk
 credit spread risk

1. Credit option
2. Credit forward
3. Credit swap
 1. option can be on spread or price
 2. forwards where payment depends on credit spread at maturity
 3. CDS  pay premium and receive in event of default

change in foreign bond value in a domestic portfolio
 duration * Byield * change in domestic yield * 100
 Yield beta = regression of foreign yield on domestic yield (beta term)

interest rate parity
F [d/f] = S [d/f] * (1+rd/1+rf)

