PrevioRisk

What is Delta Equivalent?

The delta equivalents of a position describe the response of a position/portfolio to a change in the market data.

Delta equivalent is the derivative of the Present Value with respect to a given risk factor, multiplied by the value (price) of that particular risk factor:
b3_0

Delta equivalent value is based on:

  • For equities, currencies and commodities: % price change in the underlying price series;
  • In the case of interest rates: % price changes in the price of the corresponding zero-coupon bond for each key rate point on the discount curve.
  •  

    Present Value response can be computed as:
    b3_1
    Delta Equivalents are additive, i.e. you can add values to get effect on entire portfolio.
    b3_2
    Note: Delta Equivalent is an approximation.

    Examples:

  • If the value of market factor changes by 100%, then Present Value of the position would change by Latex formula USD.
  • If the values of market factors A and B change by 1% and 2%, respectively, then Present Value of the position would change by 0.01* Latex formula+ 0.02* Latex formula USD.
  • If the value of 4-year zero-coupon USD Goverment bond increases by 1% in absolute amount, then 5-year bond’s price (which has USD Government bond as underlying risk factor) would change approximately by 0.01*Latex formula.
  • Example below shows that 1% decrease of EUR/USD exchange rate would change the portfolio value by 1,312,736/0.01=13,127 USD.
  • b3_4

    In case only yield change is known, we can convert price sensitivities to yield sensitivities: b3_5,
    where B is bond price, D – duration, y – yield. Thus:

  • If yield for InterestRate\EUR Govt 24M (in the table above) increases by 0.01% (1bp), then PV of the portfolio would change by -2*0.0001*1,312,726=262 USD.
  • If the yield of the 4-year zero-coupon USD Goverment bond decreases by 25bp, then the 5-year bond’s yield would change approximately by -4*0.0025*(USD Govt 4Y).

  • See also: help.riskmetrics.com


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