Every portfolio manager wishes to construct predictable & manageable portfolios that are less risky, profitable & with less investment. This is going to be a uphill task given that many types & number of instruments are present in the portfolio. In this post we have demonstrated tools which helps in improving predictability.
Anecdote:- In real life Best Friend[Portfolio Manager] knows the possible reasons for your[Portfolio]Mood Swings.What would have made you feel down :).
Decompose Portfolio Risk Why ? Rationale behind this!!!
Keeping track of portfolio risk becomes cumbersome when number of instruments increases. With the help of P&L Attribution or P&L Explain Portfolio Risk can be managed easily as it attributes or explains daily fluctuation in value of a portfolio of trades to the root cause.
P&L Attribution in One Line!!
Portfolio P&L = P&LExplainedByRiskFactors + UnExplainedP&L
How? P&L Attribution!![Choose=>Map=> Aggregate]
Instead of trying to determine Risk of each instrument, decompose these instruments into
primitive instruments which is used to calculate Regulatory Capital also. Overview:-
1) Choose : Set of elementary risk factors & estimate their probability distributions.
2) Map : Find common RiskFactors among positions in a given portfolio. Map
financial instruments into exposures on these risk factors.
[i.e.Each Position is marked to market,value of each instrument is allocated to risk factors.]
3) Aggregate : Aggregate the exposure for all positions & build distribution of P/L on portfolio.
RiskFactor should be a principal determinant of change in value of a transaction used for quantification of risk.Usually, Factors that are deemed relevant for pricing should be included as Risk Factors.
Factors to be considered:-
Based on type of Instrument Asset Class, you can decide which RiskFactors to be used. Guidelines below(not exhaustive though):-
| Asset Class | Risk Factors | ||
| Interest Rates | 1) RiskFactor corresponding to each maturity segment of yield curve. | ||
| Forex Rates | 1) RiskFactors corresponding to individual foreign currency in which bank's currency are denominated. 2) RiskFactors corresponding to exchange rate risk. | ||
| Equity Prices | 1) RiskFactors capturing market—wide movements in equity prices (e.g S&P 500,..etc). 2) RiskFactors capturing sector-wide movements in equity prices (e.g.Manufacturing,Pharma.etc). 3) RiskFactors corresponding to volatility of individual security. | ||
| Commodity Price | 1) RiskFactors corresponding to each of commodity markets in which banks hold significant position. 2) For banks with limited exposure following are acceptable:- a) One RiskFactor for each commodity price. (or) b) For small position, it might be acceptable to use single RiskFactor for a relatively broad sub-category of commodities. 3) RiskFactors should account variation in “”convenience yield” between derivative positions. | ||
| Credit | 1) RiskFactor to incorporate spread risk(eg between bonds & swaps). | ||
Example:-
See below an example of how instruments are mapped to RiskFactors and their exposure measures.(More detailed in the next post).
| RiskFactors | ||||
| Instrument | Change in Interest Rate | Change in Equity Index Price | ||
| Fixed Income Security | Modified Duration Convexity |
|||
| Equities | Beta=1.5 | |||
Change in Equity Index Price has no impact on Fixed Income Security.
Increase in Equity Index Price has corresponding positive impact on Equities price.(+1.5)
Increase in Equity Index Price has corresponding positive impact on Equities price.(+1.5)
Effectiveness Metrics:-
To determine whether risk factors included in captures material drivers of bank's actual P&L effectively,use:-
1) Average P&L left UnExplained as a unit of Dispersion of Actual P&L.
Mean of UnExplained P&L[Predicted P&L - Actual P&L ]
Mean of UnExplained P&L[Predicted P&L - Actual P&L ]
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StandardDeviation of Actual P&L.
2)Variance of P&L left UnExplained as a unit of Variance of Actual P&L.
Variance of UnExplained P&L
Variance of UnExplained P&L
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Variance of Actual P&L
Both measures quantify the impact of Actual P&L dispersion on P&L Attribution Accuracy.
Advantages:-
1) Assist the risk manager in evaluating positions whose characters may change over time.
2) Assist the risk manager in evaluating positions even in absence of long history.
3) Assist the risk manager in evaluating positions by reducing number of variables.
Conclusion:-
RiskFactor mapping is an effective way in managing & measuring portfolio risk. This effectiveness can be felt when the portfolio size is bigger, portfolio contains many types of instruments, instruments having unique behaviors...etc.
To Be Continued....:-
In the next post we will delve deep into factor exposures and see how to use those factor exposures in quantifying risk,predicting returns,,..etc. How to predict the portfolio risk in a better way using the exposures, riskfactors,.etc.
Appendix:-
Risk-Theoretical P&L is defined as the daily desk-level (hypothetical) P&L that is predicted by the risk management model conditional on a realisation of all relevant risk factors that enter the model.
