大浩浩的笔记课堂——FRM考试学习笔记136

Topic 65 Portfolio Risk:Analytical Methods

1.Portfolio VaR measures:

⑴portfolio VaR ＆ individual VaR:

①portfolio VaR:

②individual VaR:

A.definition:

It is the VaR of an individual position in isolation.

B.formula:

⑵diversified VaR ＆ undiversified VaR:

①diversified VaR:

A.definition:

Taking into account diversification benefits between components.

B.formula:

②undiversified VaR:

A.definition:

The portfolio VaR when there is no short position and all correlations are unity.

B.formula:

2.VaR tools(Other portfolio VaR measures):

⑴marginal VaR(Δ=1):

①definition:

It is the per dollar change in portfolio VaR that occurs from an additional investment in as position.

②formula:

③usage:

How to use it:

A.obtain the optimal portfolio:

Equating the excess return/MVaR ratio of all portfolio positions.

B.obtain the lowest portfolio VaR:

Equating just the MVaRs of all portfolio positions.

⑵incremental VaR(Δ=any $):

①definition:

It is a change in VaR from the addition of a new position in a portfolio.

②formula:

③characteristic:

A.It is the change in VaR owing to a new position.

B.It differs from the marginal VaR in that the amount added or subtracted can be large,in which case VaR changes in a nonlinear fashion.

C.Comparing to using marginal VaRs,computing with full revaluation is more costly,but also more accurate.

④usage:

It applies to the general case where a trade involves a set of new exposes on the risk factors.

⑤drawback:

It requires a full revaluation of the portfolio VaR with new trade.

⑥best hedge:

A.The best hedge is additional amount to invest in an asset so as to minimize the risk of the total portfolio.

B.less costly approximation method:

a/ Breaking down the new position into risk factors.

b/ Multiplying each new risk factor times the corresponding partial derivative of the portfolio with respect to factors.

c/ Adding up all the values.

⑶component VaR(Δ=p_i):

①definition:

It is the amount of risk a particular fund contributes to a portfolio of funds.(not elliptical)

②formula:

③characteristic:

A partition of the portfolio VaR that indicates how much the portfolio VaR would change approximately if the given component was deleted by construction,component VaRs sum to the portfolio VaR.

3.Examples:

⑴A Global Portfolio Equity Report

⑵Barings:An Example in Risks

4.Managingportfoliosusing VaR:

⑴from risk measurement to risk management:

①changing:

A.Positions should be cut first where the marginal VaR is the greatest,keeping portfolio constraints satisfied.

B.With the lowest marginal VaR,it should be added to make up for the first charge.

②repeating:

Repeating process until reached a global minimum.

③verifying:

The betas of all positions are equal when risk is minimized.

·特别注意！

·for lowest portfolio VaR:

The MVaRs of all portfolio positions must be equal.

⑵from risk management to portfolio management:

for optimal portfolio(portfolio risk will be at a global minimum):

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