1. Measuring Risk Risk Management Prof. Ali Nejadmalayeri, Dr N a.k.a. “Dr N”

2. Risk & Return of Securities Assuming that current price is P 0 and the security can be sold for P 1, then: distribution mean expected value, E[r] varianceE[r – E[r]] 2If this return is random, then over time, we can see what is its distribution. The central tendency of the distribution is mean. If this distribution is true and stable, then this mean is our measure of expected value, E[r]. One measure of variation of our random return is variance, E[r – E[r]] 2. standard deviationAnother measure of volatility is standard deviation which squared root of the variance.

3. Probability & Distribution Given that we know the distribution of returns, then we can compute cumulative probabilities of returns being below certain thresholds!

4. Excel & CDFs Imagine, IBM has an average return of 10% and standard deviation of 30%. What is probability of a loss? –Use NORMDIST function in Excel Enter

5. CDF vs. PDF Cumulative Distribution Functions represent probability of up to an outcome whereas Probability Density Functions represent probability of one outcome!

6. Portfolio Return Imagine N assets with returns, r i, are combined such that w i fraction of total funds is invested in each of the assets, then the portfolio’s return is: Then for expected return of the portfolio, we have:

7. Portfolio Variance Imagine that each pair of assets in a portfolio with N assets with returns, r i, and asset weight, w i, has a correlation of ρ ij, then the variance of the portfolio is:

8. Diversification Unlike return, variance of a portfolio is also related to correlations. So if these correlations different from ONE, then there can be some risk saving!

9. Efficient Frontier When assets are combined, the possible return-risk outcomes form an efficient frontier on which best return for any level risk or vice versa lowest risk for any level return is obtained!

10. Risk & Asset Pricing If idiosyncratic risk can be removed by creating well-diversified portfolios, then only correlations with market risk should matter for determining return! Then return on each asset is given by:

11. Valuation & CAPM Assume a firm generates E[C] of cash flows. If the firm is all equity financed, then value of the firm is defined by:

12. Risk Management & Value If risk management reduces risk, then value can increase; lower discount rate! –By prudent diversification schemes, idiosyncratic risk can be eliminated In perfect markets, both investors and firms can do this, so the shouldn’t be reward associated with risk management in perfect markets –By taking short or offsetting positions, systematic risk can be eliminated In perfect markets, both investors and firms can do this, so the shouldn’t be reward associated with risk management in perfect markets

13. Why Manage Risk? Hedging Irrelevance Proposition:Hedging Irrelevance Proposition: –When the cost of bearing risk is same for firms and individuals, hedging cannot add value! Risk management is only beneficial only if firms can perform hedging at lower cost than their shareholders.

14. A Helicopter View Uncertainty is a fact of life, so there is no crystal ball! But risk can be managed! Indentify Risk Exposures Measure and Estimate Risk Exposures Find Instruments & Facilities to Shift or Trade Risk Asset Effects of Exposures Assess Costs & Benefits of Instruments From a Risk Mitigation Strategy: Avoid, Transfer, Mitigate, Keep Evaluate Performance

15. Topology of Risk Risks Legal & Regulatory Risk Operational Risk Liquidity Risk Credit Risk Market Risk Strategic Risk Reputation Risk Business Risk

16. Financial Risks Market Risk Credit Risk Equity Price Risk Interest Rate Risk Currency Risk Commodity Risk Trading Risk Portfolio Concentration Transaction Risk Gap Risk General Market Risk Specific Risk