FRM Zvi Wiener Following P. Jorion, Financial Risk Manager Handbook Financial Risk Management

FRM Chapter 13 Sources of Risk Following P. Jorion 2001 Financial Risk Manager Handbook

Ch. 13, HandbookZvi Wiener slide 3 Currency Risk free movements of currency devaluation of a fixed or pegged currency regime change (Israel, Europe)

Ch. 13, HandbookZvi Wiener slide 4 Currency Volatility End 99End 96 Argentina Australia Canada Switzerland1010 Denmark Britain Hong Kong Indonesia241.6 Japan116.6 Korea6.94.5

Ch. 13, HandbookZvi Wiener slide 5 Currency Volatility End 99End 96 Mexico7.57 Malaysia Norway New Zealand Philippines Sweden Singapore Thailand Taiwan Euro S. Africa4.28.4

Ch. 13, HandbookZvi Wiener slide 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

Ch. 13, HandbookZvi Wiener slide 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

Ch. 13, HandbookZvi Wiener slide 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%

Ch. 13, HandbookZvi Wiener slide 9 Cross Rate volatility JPY/USD = xJPY/DEM = yDEM/USD = z

Ch. 13, HandbookZvi Wiener slide 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

Ch. 13, HandbookZvi Wiener slide 11 Volatilities of IR/bond prices Price volatility in %End 99End 96 Euro 30d Euro 180d Euro 360d Swap 2Y Swap 5Y Swap 10Y Zero 2Y Zero 5Y Zero 10Y Zero 30Y

Ch. 13, HandbookZvi Wiener slide 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%).

Ch. 13, HandbookZvi Wiener slide 13 Models of IR Normal model  (  y) is normally distributed. Lognormal model  (  y/y) is normally distributed. Note that:

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 15 Volatilities of yields Yield volatility in %, 99  (  y/y)  (  y) Euro 30d452.5 Euro 180d Euro 360d90.57 Swap 2Y Swap 5Y Swap 10Y Zero 2Y Zero 5Y Zero 10Y Zero 30Y

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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 8/32Accrued 1.43% Yield 6.509%Duration Modified Dur Yield volatility 12% A. $291,400 B. $203,080 C. $206,036 D. $206,698

Ch. 13, HandbookZvi Wiener slide 19 FRM-99, Question 80 Value of the position Daily yield volatility

Ch. 13, HandbookZvi Wiener slide 20 Correlations Eurodeposit block zero-coupon Treasury block very high correlations within each block and much lower across blocks.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 22 FRM-00, Question 96 Which statement about historic US Treasuries yield curves is TRUE?

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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!

Ch. 13, HandbookZvi Wiener slide 31 Fixed income portfolio risk Yield curve component (government) Credit spread (of the class of similar rating) Specific spread

Ch. 13, HandbookZvi Wiener slide 32 Equity risk Market risk (beta based relative to an index) Specific risk

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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. values

Ch. 13, HandbookZvi Wiener slide 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 S t - D, where D is the PV of the dividend.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 38 In an equilibrium the following holds (Sharpe) CAPM

Ch. 13, HandbookZvi Wiener slide 39 APT Arbitrage Pricing Theory

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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 % yearly volatility (much less storable). Long forward prices are less volatile then short forward prices.

Ch. 13, HandbookZvi Wiener slide 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

Ch. 13, HandbookZvi Wiener slide 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

Ch. 13, HandbookZvi Wiener slide 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.

Ch. 13, HandbookZvi Wiener slide 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