Assignment for financial risk management must be done on EXCEL file. 6 problems, and the Q4 has another spredsheet "Greek" needs to be provided to you but I could not upload two files.
Assignment 2 Financial Risk Management I Instruction: you should submit an Excel spreadsheet for this assignment. Each worksheet includes your solution to one problem and titled accordingly, e.g., “Q1” “Q4”, etc. Problem Points 1 1 2 1 3 1 4 1 5 0.5 6 0.5 Total 5 1. Portfolio A consists of $5,000 investment in a 1-year zero-coupon bond and $20,000 investment in a 20-year zero-coupon bond. Portfolio B consists of a 10-year zero-coupon bond with a face value of $17,000. The current yield on all bonds is 4% per annum (continuously compounded). a. Compute the actual percentage changes in the values of the two portfolios for a 20-basis point increase in yields. b. Compute the actual percentage changes in the values of the two portfolios for a 200-basis point increase in yields. c. Compute the duration for each portfolio. Use these durations to forecast the change in the value of each portfolio for a 20-basis point and a 200-basis point increase in yields. d. Compute the convexities for each portfolio. Use duration and convexity to forecast the change in the value of each portfolio for a 20-basis point and a 200-basis point increase in yields. e. Find the percentage forecast errors from c and d. Discuss your results. 2. Suppose that the parameters in a GARCH(1,1) model are = 0.04, = 0.94, and = 0.000003. a. What is the long-run average volatility? b. If the current volatility is 2% per day, what is your estimate of the volatility in 30, 60, and 120 days? c. Suppose volatility suddenly increases from 2% per day to 3%. Estimate the effect on our volatility forecasts in 30, 60, and 120 days. 3. Use the Greek calculator spreadsheet (Option type: Black-Scholes European) for this problem. You will also need market data on SPY and its options, found in the following links: https://finance.yahoo.com/quote/SPY?p=SPY https://finance.yahoo.com/quote/SPY/options?p=SPY You are considering a position that consists of European at-the-money call and at-the-month put options[footnoteRef:1], with an expiration date of the third Friday of the next closest month. (If it is September now, the option expires in the third Friday of October). Assume the standard deviation of SPY is 20% over the next month. Risk-free rate is 1%, and SPY dividend yield is 1.5%. [1: At the money (ATM) option is the option whose strike price is closest to the price of the underlying security. Find the closest option to the underlying price from the option’s page link provided in the question.] a) Compute a fair price for the call and put options and the associated Greeks. b) We buy 100 of the ATM put. We need add to 100 ATM calls to create the straddle position. What should the weights for the ATM call be so that the resulting portfolio is delta-neutral? This is known as a delta-neutral straddle position. By how much will the value of the delta-neutral straddle position change if the SPY’s standard deviation increase from 20% to 22%? 4. Suppose that the change in a portfolio value for a one‐basis‐point shift in the 1‐, 2‐, 3‐, 4‐, 5‐, 7‐, 10‐, and 30‐year rates are (in $ millions) -3, -2, -1 , +1, +3, +5, +7, and +8, respectively. Estimate the delta of the portfolio with respect to the first three Principal Component factors of the following Table. Quantify the relative importance of the three factors for this portfolio. Factor loadings PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 1‐year 0.22 -0.50 0.63 -0.49 0.12 0.24 0.01 -0.03 2‐year 0.33 -0.43 0.13 0.35 -0.21 -0.67 -0.10 0.24 3‐year 0.37 -0.27 -0.16 0.41 -0.10 0.31 0.41 -0.56 4‐year 0.39 -0.11 -0.26 0.17 -0.02 0.55 -0.42 0.51 5‐year 0.40 0.02 -0.36 -0.27 0.60 -0.28 -0.32 -0.33 7‐year 0.39 0.19 −0.195 -0.34 0.01 -0.10 0.69 0.42 10‐year 0.38 0.37 0.07 -0.31 -0.68 -0.04 -0.28 -0.28 30‐year 0.31 0.55 0.58 0.40 0.33 0.02 0.01 0.03 Standard deviation of factor scores PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 17.55 4.77 2.08 1.29 0.91 0.73 0.56 0.53 5. The probability that the loss from a portfolio will be greater than $10 million in one month is estimated to be 1%. a) What is the loss that has a 0.1% chance of being exceeded, assuming the change in value of the portfolio is normally distributed with zero mean? b) What is the loss that has a 0.1% chance of being exceeded, assuming the power law applies with α = 3? 6. Use the data in https://cfe.cboe.com/cfe-products/vx-cboe-volatility-index-vix-futures. a. Plot the current term structure of volatility using VIX future contracts. From this table only use the spot (^VIX) and the monthly contracts (those with 5 letter symbols) to plot the term structure. b. What type of information can we infer from this graph? c. Although the volatility term structure takes any shape, it is usually upward sloping. How do you interpret this empirical finding? 61