Zvi Wiener

1
Financial Risk Management

• Zvi Wiener
• Following
• P. Jorion, Financial Risk Manager Handbook

2
Chapter 13Sources of Risk

• Following P. Jorion 2001
• Financial Risk Manager Handbook

3
Currency Risk

• free movements of currency
• devaluation of a fixed or pegged currency
• regime change (Israel, Europe)

4
Currency Volatility

• End 99 End 96
• Argentina 0.35 0.4
• Australia 7.6 8.5
• Canada 5.1 3.6
• Switzerland 10 10
• Denmark 9.8 7.8
• Britain 6.5 9.1
• Hong Kong 0.3 0.3
• Indonesia 24 1.6
• Japan 11 6.6
• Korea 6.9 4.5

5
Currency Volatility

• End 99 End 96
• Mexico 7.5 7
• Malaysia 0.1 1.6
• Norway 7.6 7.6
• New Zealand 13.4 7.9
• Philippines 5.5 0.6
• Sweden 8.5 6.4
• Singapore 3.8 1.8
• Thailand 9.7 1.2
• Taiwan 1.8 0.9
• Euro 9.8 8.3
• S. Africa 4.2 8.4

6
FRM-97, Question 10

• Which currency pair would you expect to have the
  lowest volatility?
• A. USD/DEM
• B. USD/CAD
• C. USD/JPY
• D. USD/ITL

7
FRM-97, Question 10

• Which currency pair would you expect to have the
  lowest volatility?
• A. USD/DEM
• B. USD/CAD
• C. USD/JPY
• D. USD/ITL

8
FRM-97, Question 14

• What is the implied correlation between JPY/DEM
  and DEM/USD when given the following volatilities
  for foreign exchange rates?
• JPY/USD 8, JPY/DEM 10, DEM/USD 6
• A. 60
• B. 30
• C. -30
• D. -60

9
Cross Rate volatility

• JPY/USD x JPY/DEM y DEM/USD z

10
Fixed Income Risk

• Arises from potential movements in the level and
  volatility of bond yields.
• Factors affecting yields
• inflationary expectations
• term spread
• higher volatility of the low end of TS

11
Volatilities of IR/bond prices

• Price volatility in End 99 End 96
• Euro 30d 0.22 0.05
• Euro 180d 0.30 0.19
• Euro 360d 0.52 0.58
• Swap 2Y 1.57 1.57
• Swap 5Y 4.23 4.70
• Swap 10Y 8.47 9.82
• Zero 2Y 1.55 1.64
• Zero 5Y 4.07 4.67
• Zero 10Y 7.76 9.31
• Zero 30Y 20.75 23.53

12
Duration approximation

• What duration makes bond as volatile as FX?
• What duration makes bond as volatile as stocks?
• A 10 year bond has yearly price volatility of 8
  which is similar to major FX.
• 30-year bonds have volatility similar to equities
  (20).

13
Models of IR

• Normal model ?(?y) is normally distributed.
• Lognormal model ?(?y/y) is normally distributed.
• Note that

14
Time adjustment

• Square root of time adjustment is more
  questionable for bond prices than for other
  assets
• there is a strong evidence of mean reversion
• bond prices converge approaching maturity
  (bridge effect) - strong for short bonds, weak
  for long.

15
Volatilities of yields

• Yield volatility in , 99 ?(?y/y) ?(?y)
• Euro 30d 45 2.5
• Euro 180d 10 0.62
• Euro 360d 9 0.57
• Swap 2Y 12.5 0.86
• Swap 5Y 13 0.92
• Swap 10Y 12.5 0.91
• Zero 2Y 13.4 0.84
• Zero 5Y 13.9 0.89
• Zero 10Y 13.1 0.85
• Zero 30Y 11.3 0.74

16
FRM-99, Question 86

• For computing the market risk of a US T-bond
  portfolio it is easiest to measure
• A. yield volatility, because yields have positive
  skewness.
• B. price volatility, because bond prices are
  positively correlated.
• C. yield volatility for bonds sold at a discount
  and price volatility for bonds sold at a premium.
• D. yield volatility because it remains more
  constant over time than price volatility, which
  must approach zero at maturity.

17
FRM-99, Question 86

• For computing the market risk of a US T-bond
  portfolio it is easiest to measure
• A. yield volatility, because yields have positive
  skewness.
• B. price volatility, because bond prices are
  positively correlated.
• C. yield volatility for bonds sold at a discount
  and price volatility for bonds sold at a premium.
• D. yield volatility because it remains more
  constant over time than price volatility, which
  must approach zero at maturity.

18
FRM-99, Question 80

• You have position of 20M in the 6.375 Aug-27 US
  T-bond. Calculate daily VaR at 95 assume that
  there are 250 business days in a year.
• Price 98 8/32 Accrued 1.43
• Yield 6.509 Duration 13.133
• Modified Dur. 12.719 Yield volatility 12
• A. 291,400
• B. 203,080
• C. 206,036
• D. 206,698

19
FRM-99, Question 80

• Value of the position

Daily yield volatility
20
Correlations

• Eurodeposit block
• zero-coupon Treasury block
• very high correlations within each block and much
  lower across blocks.

21
Principal component analysis

• level risk factor 94 of changes
• slope risk factor (twist) 4 of changes
• curvature (bend or butterfly)
• See book by Golub and Tilman.

22
FRM-00, Question 96

• Which statement about historic US Treasuries
  yield curves is TRUE?

23
FRM-00, Question 96

• A. Changes in the long-term yield tend to be
  larger than in short-term yield.
• B. Changes in the long-term yield tend to be
  approximately the same as in short-term yield.
• C. The same size yield change in both long-term
  and short-term rates tends to produce a larger
  price change in short-term instruments when all
  securities are traded near par.
• D. The largest part of total return variability
  of spot rates is due to parallel changes with a
  smaller portion due to slope changes and the
  residual due to curvature changes.

24
FRM-00, Question 96

• A. Changes in the long-term yield tend to be
  larger than in short-term yield.
• B. Changes in the long-term yield tend to be
  approximately the same as in short-term yield.
• C. The same size yield change in both long-term
  and short-term rates tends to produce a larger
  price change in short-term instruments when all
  securities are traded near par.
• D. The largest part of total return variability
  of spot rates is due to parallel changes with a
  smaller portion due to slope changes and the
  residual due to curvature changes.

25
FRM-97, Question 42

• What is the relationship between yield on the
  current inflation-proof bond issued by the US
  Treasury and a standard Treasury bond with
  similar terms?
• A. The yields should be about the same.
• B. The yield on the inflation protected bond
  should be approximately the yield on treasury
  minus the real interest.
• C. The yield on the inflation protected bond
  should be approximately the yield on treasury
  plus the real interest.
• D. None of the above.

26

• Credit Spread Risk
• Prepayment Risk (MBS and CMO)
• seasoning
• current level of interest rates
• burnout (previous path)
• economic activity
• seasonal patterns
• OAS option adjusted spread spread over
  equivalent Treasury minus the cost of the option
  component.

27
FRM-99, Question 71

• You held mortgage interest only (IO) strips
  backed by Fannie Mae 7 percent coupon. You want
  to hedge this by shorting Treasury interest
  strips off the 10-year on-the-run. The curve
  steepens as 1 month rate drops, while the 6
  months to 10 year rates remain stable. What will
  be the effect on the value of your portfolio?
• A. Both IO and the hedge appreciate in value.
• B. Almost no change in both (may be a small
  appreciation).
• C. Not enough information to find changes in
  both.
• D. The IO will depreciate, the hedge will
  appreciate.

28
FRM-99, Question 71

• You held mortgage interest only (IO) strips
  backed by Fannie Mae 7 percent coupon. You want
  to hedge this by shorting Treasury interest
  strips off the 10-year on-the-run. The curve
  steepens as 1 month rate drops, while the 6
  months to 10 year rates remain stable. What will
  be the effect on the value of your portfolio?
• A. Both IO and the hedge appreciate in value.
• B. Almost no change in both (may be a small
  appreciation).
• C. Not enough information to find changes in
  both.
• D. The IO will depreciate, the hedge will
  appreciate.

29
FRM-99, Question 73

• A fund manager attempting to beat his LIBOR based
  funding costs, holds pools of adjustable rate
  mortgages and is considering various strategies
  to lower the risk. Which of the following
  strategies will NOT lower the risk?
• A. Enter a total rate of return swap swapping the
  ARMs for LIBOR plus a spread.
• B. Short US government bonds
• C. Sell caps based on the projected rate of
  mortgage paydown.
• D. All of the above.

30
FRM-99, Question 73

• A fund manager attempting to beat his LIBOR based
  funding costs, holds pools of adjustable rate
  mortgages and is considering various strategies
  to lower the risk. Which of the following
  strategies will NOT lower the risk?
• A. Enter a total rate of return swap swapping the
  ARMs for LIBOR plus a spread.
• B. Short US government bonds.
• C. Sell caps based on the projected rate of
  mortgage paydown.
• D. All of the above.

He should buy caps, not sell!
31
Fixed income portfolio risk

• Yield curve component (government)
• Credit spread (of the class of similar rating)
• Specific spread

32
Equity risk

• Market risk (beta based relative to an index)
• Specific risk

33
FRM-97, Question 43

• Which of the following statements about SP500 is
  true?
• I. The index is calculated using market prices as
  weights.
• II. The implied volatilities of options of the
  same maturity on the index are different.
• III. The stocks used in calculating the index
  remain the same for each year.
• IV. The SP500 represents only the 500 largest US
  corporations.
• A. II only. B. I and II.
• C. II and III. D. III and IV only.

34
FRM-97, Question 43

• Which of the following statements about SP500 is
  true?
• I. The index is calculated using market prices as
  weights.
• II. The implied volatilities of options of the
  same maturity on the index are different.
• III. The stocks used in calculating the index
  remain the same for each year.
• IV. The SP500 represents only the 500 largest US
  corporations.
• A. II only. B. I and II.
• C. II and III. D. III and IV only.

35
Forwards and Futures

• The forward or futures price on a stock.
• e-rt the present value in the base currency.
• e-yt the cost of carry (dividend rate).
• For a discrete dividend (individual stock) we can
  write the right hand side as St- D, where D is
  the PV of the dividend.

36
FRM-97, Question 44

• A trader runs a cash and future arbitrage book on
  the SP500 index. Which of the following are the
  major risk factors?
• I. Interest rate
• II. Foreign exchange
• III. Equity price
• IV. Dividend assumption risk
• A. I and II only.
• B. I and III only.
• C. I, III, and IV only.
• D. I, II, III, and IV.

37
FRM-97, Question 44

• A trader runs a cash and future arbitrage book on
  the SP500 index. Which of the following are the
  major risk factors?
• I. Interest rate
• II. Foreign exchange
• III. Equity price
• IV. Dividend assumption risk
• A. I and II only.
• B. I and III only.
• C. I, III, and IV only.
• D. I, II, III, and IV.

38
CAPM

• In an equilibrium the following holds (Sharpe)

39
APTArbitrage Pricing Theory
40
FRM-98, Question 62

• In comparing CAPM and APT, which of the following
  advantages does APT have over CAPM?
• I. APT makes less restrictive assumptions about
  investor preferences toward risk and return.
• II. APT makes no assumption about the
  distribution of security returns.
• III. APT does not rely on the identification of
  the true market portfolio, and so the theory is
  potentially testable.
• A. I only. B. II and III only.
• C. I, and III only. D. I, II, and III.

41
FRM-98, Question 62

• In comparing CAPM and APT, which of the following
  advantages does APT have over CAPM?
• I. APT makes less restrictive assumptions about
  investor preferences toward risk and return.
• II. APT makes no assumption about the
  distribution of security returns.
• III. APT does not rely on the identification of
  the true market portfolio, and so the theory is
  potentially testable.
• A. I only. B. II and III only.
• C. I, and III only. D. I, II, and III.

42
Commodity Risk

• Base metal - aluminum, copper, nickel, zinc.
• Precious metals - gold, silver, platinum.
• Energy products - natural gas, heating oil,
  unleaded gasoline, crude oil.
• Metals have 12-25 yearly volatility.
• Energy products have 30-100 yearly volatility
  (much less storable).
• Long forward prices are less volatile then short
  forward prices.

43
FRM-97, Question 12

• Which of the following products should have the
  highest expected volatility?
• A. Crude oil
• B. Gold
• C. Japanese Treasury Bills
• D. DEM/CHF

44
FRM-97, Question 12

• Which of the following products should have the
  highest expected volatility?
• A. Crude oil
• B. Gold
• C. Japanese Treasury Bills
• D. DEM/CHF

45
FRM-97, Question 23

• Identify the major risks of being short 50M of
  gold two weeks forward and being long 50M of
  gold one year forward.
• I. Spot liquidity squeeze.
• II. Spot risk.
• III. Gold lease rate risk.
• IV. USD interest rate risk.
• A. II only. B. I, II, and III only.
• C. I, III, and IV only. D. I, II, III, and IV.

46
FRM-97, Question 23

• Identify the major risks of being short 50M of
  gold two weeks forward and being long 50M of
  gold one year forward.
• I. Spot liquidity squeeze.
• II. Spot risk.
• III. Gold lease rate risk.
• IV. USD interest rate risk.
• A. II only. B. I, II, and III only.
• C. I, III, and IV only. D. I, II, III, and IV.

Spot risk is eliminated by offsetting positions