VaR

1
VaR by example

• Zvi Wiener
• 02-588-3049
• http//pluto.mscc.huji.ac.il/mswiener/zvi.html

2
Assets

• NIS TSAMUD Yen
• Deposit 1yr. 6 4,000
• Bonds 10yr. 5 2,000
• Credit 3yr. 15 8,000

Liabilities
Today L6
NIS TSAMUD Yen Saving 2yr. 4
1,800 Deposit 1mo. 11 8,200 Deposit 3mo.
L-2 3,000
Total (200) 200 4,000 (3,000)
3
Assets

• NIS TSAMUD Yen
• Deposit 1yr. 6 4,000
• Bonds 10yr. 5 2,000
• Credit 3yr. 15 8,000

Liabilities
Today L6
NIS TSAMUD Yen Saving 2yr. 4
1,800 Deposit 1mo. 11 8,200 Deposit 3mo.
L-2 3,000
Total (200) 200 4,000 (3,000)
4
Risk Factors

• USD/NIS exchange rate
• Yen/NIS exchange rate
• Inflation
• Real NIS interest rates (IR, 10 yr., 2 yr.)
• Nominal NIS IR (1mo., 10 yr.)
• USD IR, (1 yr.)
• Yen IR, (Libor 3 mo.)

5
Fair Value

• For risk measurement we need not only the fair
  value, but the fair value as a function of risk
  factors in order to estimate the potential
  profit/loss.

6
Fair Value Function
7
Fair Value Function
8
Fair Value Function
9
Sensitivity

• CPI
• USD
• Yen
• rnominal1mo
• rnominal3yr
• rreal2yr
• rreal10yr
• rUSD1yr
• rYen3mo

0.1 1 2 0.5 0.5 0.5 0.5 0.25 0.25
-8 40 -60 3 -103 17 -93 -10
2
10
Risky Scenario
11
Sensitivity

• CPI
• USD
• Yen
• rnominal1mo
• rnominal3yr
• rreal2yr
• rreal10yr
• rUSD1yr
• rYen3mo

0.1 1 2 0.5 0.5 0.5 0.5 0.25 0.25
-8 40 -60 3 -103 17 -93 -10
2
12
Gradient Vector

• Direction of fastest decay (loss).
• Take the sensitivity vector and divide it by the
  assumed changes in the risk factors.

13
What if ...

• The sensitivity vector allows to estimate quickly
  an impact of a certain market move on the value
  of the portfolio.
• Scalar multiplication of the gradient vector and
  the hypothetical market change vector gives the
  predicted loss/gain.

14
Risk Management

• Swap Dollar Yen
• Two forward contracts
• Quanto option
• FRA (?)
• Fixed - floating swap