08FRM HandBook Key Concepts

来源：Kaplan Schweser　作者：Vivian 　时间：2008-09-10　点击：

Quantitative Analysis

Bond Fundamental

For Fixed present value and cash flows, increasing the frequency of the compounding will decrease the associated yield (P5)
Dollar duration measures the (negative) slope of the tangent to the price-yield curve at the starting point (P12)
Convexity is always positive for regular coupon-paying bonds. Greater convexity is beneficial both for falling and rising yields (P13)
(Macaulay) duration represents an average of the time to wait for all cash flows (P16)
The duration of a long-term bond can be approximated by an upper bound, which is that of a consol with the same yield, Dc=(1+y)/y (P18)

Fundamentals of Probability
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The expectation of a sum is the sum of expectations. The variance of a sum, however, is only the sum of variances if the variables are uncorrelated (42)
With normal distributions, the VAR of a portfolio is obtained from the product of the portfolio standard deviation and a standard normal deviate factor that reflects the confidence level – for instance 1.645 at the 95% level (49)
A linear combination of jointly normal variables has a normal distribution (49)
When successive returns are uncorrelated, the volatility increases as the horizon extends following the square root of time (68)
With independent draws, the standard deviation of most statistics is inversely related to the square root of number of observations T. Thus, more observations make for more precise estimates.

Capital Markets

The forward price differs from the spot price to reflect the time value of money and the income yield on the underlying asset. It is higher than the spot price if the yield on the asset is lower than the domestic risk-free interest rate, and vice versa.(115)
The current value of an outstanding forward contract can be found by entering an offsetting forward position and discounting the net cash flow at expiration. (115)
A long position in an asset is equivalent to a long position in a European call with a short position in an otherwise identical put, combined with a risk-free position (128)
An American call option on a non-dividend-paying stock (or asset with no income) should never be exercised early. If the asset pays income, early exercise may occur, with a probability that increases with the size of the income payment. (134)
An American put option on a non-dividend-paying stock (or asset with no income) may be exercised early. If the asset pays income, the possibility of early exercise decreases with the size of the income payments. (135)
With an option on futures, the implicit income is the risk-free rate of interest (140)
The duration of a floating-rate note is the time to wait until the next reset period, at which time the FRN should be at par (162)
In an upward-sloping term-structure environment, the forward curve is above the spot curve, which is above the par yield curve. According to the expectations hypothesis, this implies a forecast for rising interest rates.(166)
Mortgage investments have negative convexity, which reflects the short position in an option granted to the homeowner to repay early. This creates extension risk when rates increase or contraction risk when rates fall. (171)
Tranching rearrange the total cash flows, total value, and total risk of the underlying securities. At all times, the total cash flows, value, and risk of the tranches must equal those of the collateral. If some tranches are less risky than the collateral, others must be more risky. (177)
A long FRA position benefits from an increase in rates. A short FRA position is similar to a long position in bond. Its duration is positive and equal to the difference between the two maturities. (188)
A position in a receive-fixed swap is equivalent to a long position in a bond with similar coupon characteristics and maturity offset by a short position in a floating-rate note. Its duration is close to that of the fixed-rate note. (195)
A position in a receive-foreign currency swap is equivalent to a long position in a foreign currency bond offset by a short position in a dollar bond (225)
Markets are in contango if spot prices are lower than forward prices. Markets are in backwardation if spot prices are higher than forward prices. Backwardation occurs when there is high current demand for the commodity, which implies high convenience yield. (233)

Market Risk Management

VAR is the maximum loss over a target horizon such that there is a low, prespecified probability that the actual loss will be larger. (244)
VAR can be extended from a one-day horizon to T days by multiplication by the square root of time. This adjustment is valid with independent and identically distributed returns that have a normal distribution (252)
The optimal hedge is given by the negative of the beta coefficient of a regression of changes in the cash value on change in the payoff on the hedging instrument (297)
The optimal hedge with stock index futures is given by the beta of he cash position times its value divided by the notional of the future contract.(305)
The delta of an at-the-money call option is close to 0.5. Delta moves to 1 as the call goes deep in the money. It moves to zero as the call goes deep out of the money (313)
The delta of an at-the-money put option is close to -0.5. Delta moves to -1 as the put goes deep in the money. It moves to zero as the put goes deep out of the money (314)
For vanilla options, gamma is the highest, or nonlinearities are most pronounce, for the short-term at-the-money options (315)
Vega is highest for long-term at-the-money options (317)
For delta-hedged portfolio, Gamma and Theta must have opposite signs. Portfolios with positive convexity, for example, must experience time decay.(321)
The normal and lognormal distributions are very similar for short horizons or low volatilities. (335)
Every financial market experiences on e or more daily price moves of 4 standard deviations or more each year. And in any year, at least one market usually has a daily move greater than 10 standard deviations.(338)
The square root of time rule used to scale one-day returns into longer horizons is generally inappropriate when risk is time varying (342)

Investment Risk Management

Performance evaluation must take into account the component of returns that can be attributed to exposures on general market factors (or risk premia). An investment manager only adds value if the residual return, called alpha, is positive (376)
Performance evaluation can be overly optimistic if based on a sample of funds affected by survivorship, selection, or instant-history bias. The extent of survivorship bias increases with the attrition rate (377)

Credit Risk Management
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The yield spread between a corporate bond and an otherwise identical bond with no credit risk reflects the expected actuarial loss, or annual default rate times the loss given default, plus a risk premium. (457)
With a positively sloped term structure, the receiver of the floating rate (payer of the fixed rate) has a greater credit exposure than the counterparty (487)
The receiver of a low-coupon currency has greater credit exposure than the counterparty. (487)

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