DAILY HOMEWORK

Please submit daily homework (must be individual) to your TA: Mr. Xuanming Cui, email: xcui32@fordham.edu

Homework #1 Market Risk

The most common risk metric to measure the market risk is VaR (value at risk). There are several ways to compute VaR. The three most popular methods are (1) historical VaR (2) parametric VaR, and (3) factor-model VaR.

1. Choose 5 or more stocks and their 1 year historical daily prices.
2. Compute their daily returns and price changes (a.k.a. P&Ls – profit and loss), means and standard deviations.
3. Compute VaRs for individual stocks:
1. Historical VaR at 5% (for a 250-observation distribution 5% is roughly the 13th observation after sorting)
2. Parametric VaR at 5% (5% is 1.645 times the standard deviation)
4. Form a portfolio with chosen weights/shares and compute variance-covariance matrix W_P.
5. Compute VaR for the portfolio
1. Historical VaR at 5% \

i. form the portfolio first

ii. for a 250-observation distribution 5% is roughly the 13th observation after sorting)

2. Parametric VaR at 5%

i. s²_P = w' W_P w

ii. 5% is 1.645 times the standard deviation

3. Factor-model VaR at 5%

i. Run principle component (obtain factor loadings)

ii. Compute values of the two factors (or till 95% of the eigenvalues)

iii. Portfolio variance s²_P = w' B W_F B' w (then take square root and apply 1.645)

Please do not submit data or Excel but only inputs and results (I recommend you copy/paste them to Word). Also please indicate clearly the answers.

Inputs:

Assumed investment amount (e.g. $1,000,000); Portfolio weights (percentages and shares); means, standard deviations, variance-covariances; anything you feel like...

Outputs:

Individual Stocks	historical	parametric
% return
price change (P&L)

Portfolio	historical	parametric	factor
% return
price change (P&L)

[Bonus] Component VaRs and Incremental (marginal) VaRs

Homework #2 Simulations

Use the spreadsheet provided sim.xls to calculate at least 10 simulated paths of (1) one-stock, (2) two-stock portfolio, and (3) stock with random interest rates. Also, plot the sample paths.

[Bonus] Generate more paths (e.g. 100 paths) and construct/plot a histogram (e.g. 10 bins).

[Bonus++] Can you calculate the 5% “historical VaR”? (here the term “historical VaR” does not mean historical data but the method of using the histogram).

Homework #3 Credit (single name)

For your companies (get CDS quotes yourselves or from the TA),

• Use bootstrapping to obtain default probabilities (and also show lambda and Q values)
• Use the KMV method to obtain PD (probability of default) and EL (expected loss) – also show MVA (market value of assets), book value of assets, and asset volatility

Please also provide inputs to the calculations

Homework #4 Credit (portfolio) and Liquidity

Vasicek model

• Use the spreadsheet provided cdo_vasicek.xls to (and use average spread) to draw the loss distribution (5 names).
• Play with the spreadsheet provided cdo_vasicek.xls to (and use average spread) to obtain the expected tranche losses

Liqidity: KMV + Black-Scholes for liquidity

• Use the information of your companies to calculate the liquidity discount ratio (orange cells)

Report

Homework #1, 3, and 4 cover market (VaR), credit (PD and EL), and liquidity (discount) risks respectively for your chosen assets. These are the three major risks of any asset and portfolio. In this report, please summarize (in a paragraph) how your companies stand in these three risks and how your portfolio is positioned.

Next please assess how you should balance among these three risks, for example (please be creative here):

• Is there a tradeoff among these three risks? (is lower market risk at the expense of credit risk)
• How to choose optimal weights so that you can minimize all three risks?
• How is the return-risk tradeoff for all three risks (returns are important, after all)?
• etc...

You may need to do additional calculations in order to answer the above questions (and your own). Do please do that.

Your report should be short and to-the-point so it should be no longer than 1 page. It should be easy to read so use standard font size 12 and double-spaced.

Finally, please have a title, your name, and student ID at the top of the report.