Exploring other kinds of risk factors

Quantitative Risk Management in R

Alexander McNeil

Professor, University of York

Exploring other kinds of risk factors

  • So far we have looked at:
    • Calculating log-returns and aggregating log-returns over longer intervals
    • Equity data, indexes and single stocks, and foreign-exchange (FX) data
  • Two other categories of risk factors:
    • Commodities prices
    • Yields of zero-coupon bonds
Quantitative Risk Management in R

Commodities data and interest-rate data

  • Commodities such as gold and oil prices
    • Do log-returns behave like stocks?
  • Government bonds - value depends on interest rates
    • Consider yields of zero-coupon bonds as risk factors
Quantitative Risk Management in R

Bond prices

  • Let $p(t, T)$ denote the price at time $t$ of a zero-coupon bond paying one unit at maturity $T$
    • $p(0, 10)$: price at $t = 0$ of bond maturing at $T = 10$
    • $p(0, 5)$: price at $t = 0$ of bond maturing at $T = 5$
    • $p(5, 10)$: price at $t = 5$ of bond maturing at $T = 10$
Quantitative Risk Management in R

Yields as risk factors

  • The yield $y(t, T)$ is defined by the equation:

$$y(t, T) = \frac{-\ln p(t,T)} {T - t}$$

  • $y(t, 10)$: yield for a 10-year bond acquired at time $t$
  • $y(t, 5)$: yield for a 5-year bond acquired at time $t$
  • Advantage of yields: comparable across maturities $T$
  • The mapping $T$ to $y(t, T)$ is yield curve at time $t$
  • Log-returns or simple returns or yields?
Quantitative Risk Management in R

Let's practice!

Quantitative Risk Management in R

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