1. JPMorgan’s Riskmetrics and Creditmetrics
Regulatory Environment
Regulators want to control the risks of financial institutions
Although regulation is often intended to reduce risk taking, it sometimes creates perverse incentives that increase risk. For example, reserve requirements, capital requirements, deposit insurance.
Regulators are discussing internal risk models that could be used by institutions to monitor risk.
JPMorgan developed two risk management packages that could be used by institutions to manage market risk and credit risk. These packages do not coordinate the results in thinking of both market and credit risk together. 5

2. 15. Market Risk-- JPMorgan’s Riskmetrics
15.1 What is market risk?
Market risk includes the risk an institution is subject to from fluctuations in returns on its assets.
The assets include any security sold through exchanges and options on the securities.
Because there is a long history of observed returns for most assets traded on the market, one can assess probability of incurring a certain loss. RiskMetrics quantifies the probability of a loss of a given size. 5

3. Market Risk-- JPMorgan’s Riskmetrics
15.2 Value at Risk
The value at risk (VaR) is the amount an institution could lose with a given probability.
Value at risk is determined using a normal distribution. The value at risk for a 5% probability is shown below. The horizon considered as a baseline for value at risk is one day.
5% probability
VaR
Possible Loss
Value Today 5

4. Market Risk-- JPMorgan’s Riskmetrics
15.3 How do you find Value at Risk?
Because the asset returns are assumed to follow a normal distribution, we can use the characteristics about the normal distribution.
To find the VaR with a 5% probability, we simply calculate
where 1.65 comes from the normal distribution, MV is the current market value, and standard deviation, , is estimated from historical DAILY returns of the asset.
To find the VaR with a 1% probability, we simply calculate
where 2.32 comes from the normal distribution, MV is the current market value, and standard deviation, , is estimated from historical DAILY returns of the asset. 5

5. Market Risk-- JPMorgan’s Riskmetrics
15.4 Example of Value at Risk
Suppose your institution owns an asset with a present value of $1 million. The daily return of the asset has a standard deviation of 1%. What is the value at risk and how much can the institution expect to lose with a 5% probability? 5

6. Market Risk-- JPMorgan’s Riskmetrics
15.5 Portfolio of Assets
All institutions have a portfolio of assets rather than one single asset. Therefore, we need to consider the portfolio of assets at risk.
Value at Risk is defined in the same way for a portfolio as it was for an individual asset. The only difference with portfolios is that we consider how the asset are related to one another. The relation between assets is measured by correlation.
Including assets in a portfolio can allow for diversification benefits. If correlation is equal to one then there are no diversification benefits. The Basle Committee on Banking Supervision recently allowed portfolio effect across assets. The estimated correlations are subject to regulatory approval. 5

7. Market Risk-- JPMorgan’s Riskmetrics
15.6 Example of a Portfolio of Assets
Suppose your institution owned the following three assets with the given daily return standard deviations and correlations and current market values, what is the Value at Risk of each asset for a 5% probability? What is the Value at Risk of the portfolio for a 5% probability? What is the Value at Risk if all assets are perfectly correlated? What if assets have zero correlation?
Market Value Standard Deviation
Asset 1 $2 mil 0.5%
Asset 2 $4 mil 0.8%
Asset 3 $5 mil 0.2%
Corr(1,2) = 0.2 Corr(1,3)=0.4 Corr(2,3)=0.5 5

8. Market Risk-- JPMorgan’s Riskmetrics
15.7 Derivative Securities
Often an institution uses derivative securities to hedge its risks. The derivative nature of the security changes its risk evaluation.
Riskmetrics adjusts for derivatives by a factor called delta, . Delta measures how the option value will change with a change in the value of the underlying asset. For instance, the delta of an option written on the Tbill interest rate measures how the option value changes with regards to the Tbill interest rate.
Value at risk can more generally be written as 5

9. Market Risk-- JPMorgan’s Riskmetrics
15.8 Horizon Length
RiskMetrics assumes a horizon length of 1 day. Most institutions hold assets for longer than that and have an investment horizon longer than one day
RiskMetrics simply scales up the 1 day estimate of value at risk to the horizon it likes. For instance, the 5% VaR for a 10 day horizon is given
This method assumes that standard deviation is independent through time.
Christoffersen P., Diebold, and Schuermann (1998) explain why the assumption is bad for risk evaluation. First, you cannot predict volatility very well past trading days. Second, you need to aggregate correctly allowing for correlation across time such as GARCH models. 5

10. Market Risk-- JPMorgan’s Riskmetrics
15.9 Capital Requirements and Value at Risk
Banks criticized BIS for the capital requirements for equities. The capital requirements on equities, fixed income instruments, and FX were add-ons to the 8% risk-based capital ratio required on assets.
BIS readjusted their capital requirements to be compatible with JPMorgan’s internal model in 1995 which became effective in 1998:
(1) Define an adverse change as the 99th percentile rather than the 95th.
(2) Use a 10 day horizon rather than one day.
(3) The bank must set capital as the higher of
(i) last day’s VaR
(ii) average daily VaR over the past 60 days times a multiplication factor of at least 3 (some institutions are punished by a higher multiple) 5

11. Market Risk-- JPMorgan’s Riskmetrics
15.10 Example of differences in Capital Adequacy
Suppose your institution owned the following three assets with the given daily return standard deviations and correlations and current market values. How much capital would be required if the regulators only worried about the 8% rule? How much capital would be required if the regulators only based it on current VaR?
Market Value Standard Deviation
Asset 1 $2 mil 0.5%
Asset 2 $4 mil 0.8%
Asset 3 $5 mil 0.2%
Corr(1,2) = 0.2 Corr(1,3)=0.4 Corr(2,3)=0.5 5

12. Market Risk-- JPMorgan’s Riskmetrics
15.11 Backtesting
Backtesting measures how Value at risk measures compare to actual valuations.
Profits and losses of a portfolio are measured each day compared to the previous day’s Value at risk estimate. Value at risk has succeeded if today’s loss does not exceed the previous value at risk estimate.
BIS requires backtesting as a method of checking whether the internal models of risk management are effective.
Backtesting occurs over the past 250 days.
Essentially BIS counts the number of times in the past 250 days that the risk measures were not adequate. Green zone (only 4 exceptions); Yellow zone (upto 9 exceptions); Red zone (greater than 10 exceptions). A red zone indicates your capital requirements multiplication factor increases. 5

13. Market Risk-- JPMorgan’s Riskmetrics
15.12 Feasibility of RiskMetrics
Ideally you want to estimate the standard deviation of each asset and then its value at risk but with thousands of fixed income and equity assets, this is a difficult and unrealistic task. The standard deviations and correlations of foreign exchange are measured daily.
The standard deviations of fixed income assets are measured as the volatility of the interest rate times the modified duration of the fixed income instrument. So Value at Risk is defined,
where MD is the modified duration of the instrument and  is the daily standard deviation of interest rate returns.
The standard deviation of equity assets is measured using CAPM
where  is the CAPM beta of the equity instrument and  is the daily standard deviation of the market index, ie. S&P 500 5

14. Market Risk-- JPMorgan’s Riskmetrics
15.13 Weaknesses and strengths of the RiskMetrics
It assumes a normal distribution when returns are fat-tailed
It is only useful for short horizons
It allows for the benefits of diversification in the bank’s market portfolio
It does not factor in other aspects of the bank’s portfolio such as credit risk, operating risk, liquidity risk, duration exposure
It provides a method to effectively measure risk each day and for institutions to allocate capital according their riskiest portfolios. Risk-Adjusted rates of Capital can be compared. It also provides a method of controlling risk of their traders. 5

15. 16. Credit Risk-- JPMorgan’s CreditMetrics
16.1 Overview
CreditMetrics measures credit risk. Although RiskMetrics is being adopted as an internal risk measurement system, CreditMetrics is relatively new (1997) and has not yet been considered by regulators. Currently, most loans have equal risk weighting.
As with RiskMetrics, CreditMetrics finds Value at Risk.
Several differences arise between credit risk and market risk:
(i) Credit risk is not traded on an exchange so it is more difficult to estimate standard deviation.
(ii) The returns to a loan do not at all look normally distributed. The potential losses are usually much higher than the potential gains. 5

16. Credit Risk-- JPMorgan’s CreditMetrics
16.2 Value at Risk
The value at risk (VaR) is the amount an institution could lose with a given probability.
Value at risk is determined using a distribution found estimating the probability of moving credit ratings. The value at risk for a 5% probability is shown below. The horizon considered as a baseline for value at risk is ONE YEAR. Notice the distribution has a long tail compared to the normal.
5% probability
VaR
Possible Loss
Value Today 5

17. Credit Risk-- JPMorgan’s CreditMetrics
16.3 Transition Matrices
Moody’s and S&P provide credit ratings for many companies and their debt instruments. They also estimate the probability of moving from one rating to the next over a year. These probabilities are called transition probabilities.
A BBB firm has the following transition matrix
Credit rating in one year Probability
AAA .02%
AA .33%
A %
BBB %
BB 5.3%
B %
CCC %
Default % 5

18. Credit Risk-- JPMorgan’s CreditMetrics
16.4 Determining Asset values
In one year, the BBB bond has the associated probabilities of moving up or down a credit rating.
For each of these credit ratings, the BBB bond will take on different values because of the increase or decrease in credit rating.
To find the distribution of asset values, we need to find the value of the bond will take for each possible credit rating in ONE YEAR.
We need two pieces of information to estimate the value of a bond in the future. We need the spot rates for each different bond category and the recovery value of the bond if it defaults. 5

19. Credit Risk-- JPMorgan’s CreditMetrics
16.5 Example of Determining Asset values
What are the possible values of a 3 year bond in one year’s time if it has a 6% coupon and the following forward rates are given today for each of the following credit ratings. In the event of default, the bond will only recover 51.13% of face value.
AAA AA A
BBB BB B
CCC 5

20. Credit Risk-- JPMorgan’s CreditMetrics
16.6 Distribution of Asset Values
Given the transition probabilities and the asset values determined earlier, we can find the distribution of possible asset values.
Plot the distribution of asset returns. Find the average and standard deviation of the distribution of asset returns. What is the comparable VaR using standard deviation and percentiles? 5

21. Credit Risk-- JPMorgan’s CreditMetrics
16.7 Portfolio of Assets
As with RiskMetrics, the institution needs to consider their instruments as a portfolio rather than as a singular asset.
You need to know the joint probability of how the portfolio of assets move together. This is given from a joint transition matrix. For instance, for a BBB and a A bond, the transition matrix might be the following. Notice this assumes some correlation between assets. What would the probabilities be if the assets were independent? 5

22. Credit Risk-- JPMorgan’s CreditMetrics
16.8 Calculating the Value of a Portfolio of Assets in One Year
Suppose the institution has both a BBB and a single A 3 year bond. The BBB bond offers a coupon of 6% and the single A offers a coupon of 5%. Both bonds have a face value of $100. The forward rates are given below. The recovery value of the single A bond is believed to be 51.13% also. What is the value associated with each possible rating?
AAA AA A
BBB BB B
CCC 5

23. Credit Risk-- JPMorgan’s CreditMetrics
16.9 Calculating the Value of a Portfolio of Assets in One Year 5

24. Credit Risk-- JPMorgan’s CreditMetrics
16.10 Distribution of A and BBB bonds:
Plot the frequency by the portfolio value in ascending order of portfolio value. 5

25. Credit Risk-- JPMorgan’s CreditMetrics
16.11 Finding the Value at Risk:
Like the single bond, we can find the mean and standard deviation by weighting the values by the appropriate frequency. For a simpler example, suppose a firm only cared about the default and non-default state. The two bonds have the following joint distributions and joint values. Find the VaR using the percentile and standard deviation. 5

26. Credit Risk-- JPMorgan’s CreditMetrics
16.12 Implementing CreditMetrics
CreditMetrics can be used to determine limits that are often used by institutions.
Three types of limits are used: (1) Additional risk to a portfolio or marginal risk; (2) exposure size; (3) absolute risk.
Also, the capital requirements are 8% on outstanding loans. As with RiskMetrics, Value at Risk from CreditMetrics could be another method of determining how much capital an institution should hold. To date, this has not been adopted.
Bank regulators limit loan concentrations to an individual borrower to 10% of capital. Therefore, if the loan is expected to lose 40 cents on the dollar, how much capital can the bank expect to lose in the event of default if it has 10% of capital invested with this borrower? 5

27. Credit Risk-- JPMorgan’s CreditMetrics
16.13 Absolute Limits using CreditMetrics 5

28. Credit Risk-- JPMorgan’s CreditMetrics
16.14 Horizon Length
CreditMetrics estimates the distribution of asset values over a year given that an asset can migrate in its credit standings over the year.
Like RiskMetrics, you might want to consider a different horizon length.
CreditMetrics assumes that the probability of migrating from one year to the next is independent.
What is the two year probability of a bond defaulting if it has a 2% probability of defaulting and a 98% probability of not defaulting in one year? Assume there is zero correlation. Assume there is a correlation of 0.5. 5

29. Credit Risk-- JPMorgan’s CreditMetrics
16.15 Assessing the Credit Risk of assets aside from bonds
1. Receivables--Payments due from customers.
Treated as a zero coupon bond
2. Loans are treated as bonds
3. Loan Commitment
4. Financial Letters of Credit are treated like loans.
5. Swaps and Forwards 5

30. Summary of RiskMetrics and CreditMetrics
Both are viewed as contenders for assessing capital requirements for institutions in managing their market and credit risks
Neither method of risk management integrates across market and credit risk and duration mismatching is not considered.
The Basle Committee allows institutions to use RiskMetrics in assessing market risk but makes the Value at Risk much larger to be conservative.
The benefits of using these internal models is to create the correct incentives for institutions in allocating their capital. They help determine risky assets. They help determine risky portfolios. They help determine risk-taking behaviour of traders. 5