1. Portfolio Management Unit – IV Risk Management Unit – IV Risk Management

2. Unit Contents Measuring Risk - Measuring Market Risk - VaR and Advantages and Limitations of VaR Managing Risk - 9 Principles. Summarizing and Q & A

3. Measuring Risk 1. Measuring Market Risk Market risk refers to the exposure associated with actively traded financial instruments, typically those whose prices are exposed to the changes in interest rates, exchange rates, equity prices, commodity prices, or some combination thereof over the years, financial theorists have created a simple and finite set of statistical tools to describe market risk. The most widely used and arguably the most important of these is the standard deviation of price outcomes associated with an underlying asset. Usually refer to this measure as the asset’s volatility, typically represented by the Greek letter sigma ( σ ). Risk Management

4. Volatility is often an adequate description of portfolio risk, particularly for those portfolios composed of instruments with linear payoffs. In some applications, such as indexing, volatility relative to a benchmark is paramount. In those cases, our focus should be on the volatility of the deviation of a portfolio’s returns in excess of a stated benchmark portfolio’s returns, known as active risk, tracking risk, tracking error volatility, or by some simply as tracking error. Measures of primary sources of risk - For a stock or stock portfolio, beta measures sensitivity to market movements and is a linear risk measure. For bonds, duration measures the sensitivity of a bond or bond portfolio to a small parallel shift in the yield curve and is a linear measure, as is delta for options, which measures an option’s sensitivity to a small change in the value of its underlying. Risk Management

5. Second-order measures of risk deal with the change in the price sensitivity of a financial instrument and include convexity for fixed-income portfolios and gamma for options. Convexity measures how interest rate sensitivity changes with changes in interest rates. Gamma measures the delta’s sensitivity to a change in the underlying’s value. Delta and gamma together capture first- and second-order effects of a change in the underlying. For options, two other major factors determine price: volatility and time to expiration, both first-order or primary effects. Sensitivity to volatility is reflected in vega, the change in the price of an option for a change in the underlying’s volatility. Option prices are also sensitive to changes in time to expiration, as measured by theta. Risk Management

6. 2. Value at Risk During the 1990s, value at risk—or VaR, as it is commonly known—emerged as the financial service industry’s premier risk management technique. J.P. Morgan (now J.P. Morgan Chase) developed the original concept for internal use but later published the tools it had developed for managing risk. VaR is a probability-based measure of loss potential. Value at risk is an estimate of the loss (in money terms) that we expect to be exceeded with a given level of probability over a specified time period. It measures a minimum loss. The VaR is 10,000,000 at a probability of 5 percent for a given time period. All else equal, if we lower the probability from 5 percent to 1 percent, the VaR will be larger in magnitude because we expect to be exceeded with only a 1 percent probability Risk Management

7. Elements of Measuring VaR: 1. Probability Level – Either 0.05 or 0.01 (corresponding to a 95 percent or 99 percent confidence level, respectively). 2. The second important decision for VaR users is choosing the time period. Risk Management

8. Calculating VaR Step 1: μ P = wS μ S + wN μ N μ P = Expected Return of Combined Portfolio wS, wN = Percentage of Investment in Asset Classes μ S, μ N = Expected return of Asset Classes Step 2:   2 P = Variance of Combined Portfolio W = Indicates the Percentage Allocated To the Respective Classes  = Correlation  S,  N = STANDARD deviation of Asset classes Step 3:  P = (  2 P)^1/2 Risk Management

9. Estimating the Expected Return and Standard Deviation of a Portfolio Combining Two Asset Classes: Calculate Value at Risk. Risk Management

10. Answer: Risk Management

11. Advantages are that it: It captures an important aspect of risk in a single number It is easy to understand Quantifies potential losses in simple terms (a 5% chance of a loss exceeding $1 million) It has met with approval from various regulatory bodies concerned with the risks faced by financial institutions Usage is versatile (multipurpose and adaptable) Limitations include: Estimation difficulties, and sensitivity to estimation methods used Potential to create a false sense of security It tends to underestimate worst-case outcomes The VaR of a specific position doesn’t always translate well into the VaR of the overall portfolio It fails to incorporate positive outcomes, thus painting an incomplete picture. It has very limited applicability, being suitable only for linear portfolios Risk Management

12. MANAGING RISK Having established methods for the identification and measurement of risk, we turn our attention to a critical stage of any solid risk management program: that of managing risk. The key components, which by now should be somewhat intuitive to you, are as follows: An effective risk governance model, which places overall responsibility at the senior management level, allocates resources effectively and features the appropriate separation of tasks between revenue generators and those on the control side of the business. Appropriate systems and technology to combine information analysis in such a way as to provide timely and accurate risk information to decision makers. Sufficient and suitably trained personnel to evaluate risk information and articulate it to those who need this information for the purposes of decision making. Risk Management

13. A recent advertisement for the Risk Metrics Group (www.riskmetrics.com) identified the following nine principles of effective risk management: 1. There is no return without risk. Rewards go to those who take risks. 2. Be transparent. Risk should be fully understood. 3. Seek experience. Risk is measured and managed by people, not mathematical models. 4. Know what you don’t know. Question the assumptions you make. 5. Communicate. Risk should be discussed openly. 6. Diversify. Multiple risks will produce more consistent rewards. 7. Show discipline. A consistent and rigorous approach will beat a constantly changing strategy. 8. Use common sense. It is better to be approximately right than to be precisely wrong. 9. Return is only half the equation. Decisions should be made only by considering the risk and return of the possibilities. Risk Management