APRM Assignment 2
Applied Portfolio &
Risk Management
Assignment II - An analysis & back testing of
Value-at-Risk and Expected Shortfall estimates. Harry Barrett – 11411698
Sean O’Driscoll - 11366676
Robert Campbell - 11477498
Rory O’Doherty - 11356366
Sean Stapleton - 11414938
FIN30240: Applied Portfolio & Risk Management
Motivation
We will undertake an analysis of two of the most commonly used risk measures, Value-atRisk (VaR) and Expected Shortfall (ES). We chose to research these measurement metrics as the global financial system has recently undergone a period of intense volatility, which impacted hugely on how we compare and contrast risk.
VaR has always been one of the most widely used methods of measuring risk by portfolio managers and financial institutions alike. It proposes a straightforward question - "what loss level is such that we are X% sure that it will not be exceeded in N business days”? VaR is popular because it captures risk in a single number and is easy to understand, however it is not without its pitfalls.
Standard VaR calculations assume that stock returns follow a Normal Distribution, which we know to be untrue.1 It is evident that returns follow a distribution with far larger tails, and so by assuming a normal distribution we are grossly underestimating the possibility of a large shock to the market.
VaR also assigns all of its risk weight to the Xth quantile of the loss distribution, and tells us nothing about the potential for losses greater than the Xth quantile. For this reason Expected
Shortfall (also known as Conditional VaR or Expected Tail Loss) is often viewed as a more conclusive risk measure. ES can be defined as the expected loss given that the loss exceeds the equivalent VaR level. Unlike VaR, ES assigns equal weight to all quantiles greater than the specified Xth quantile.
The financial crises of 2007-08 sent shockwaves through banking systems globally, and many
U.S. and European institutions were hit with unforeseen losses. Many
Risk Management
Assignment II - An analysis & back testing of
Value-at-Risk and Expected Shortfall estimates. Harry Barrett – 11411698
Sean O’Driscoll - 11366676
Robert Campbell - 11477498
Rory O’Doherty - 11356366
Sean Stapleton - 11414938
FIN30240: Applied Portfolio & Risk Management
Motivation
We will undertake an analysis of two of the most commonly used risk measures, Value-atRisk (VaR) and Expected Shortfall (ES). We chose to research these measurement metrics as the global financial system has recently undergone a period of intense volatility, which impacted hugely on how we compare and contrast risk.
VaR has always been one of the most widely used methods of measuring risk by portfolio managers and financial institutions alike. It proposes a straightforward question - "what loss level is such that we are X% sure that it will not be exceeded in N business days”? VaR is popular because it captures risk in a single number and is easy to understand, however it is not without its pitfalls.
Standard VaR calculations assume that stock returns follow a Normal Distribution, which we know to be untrue.1 It is evident that returns follow a distribution with far larger tails, and so by assuming a normal distribution we are grossly underestimating the possibility of a large shock to the market.
VaR also assigns all of its risk weight to the Xth quantile of the loss distribution, and tells us nothing about the potential for losses greater than the Xth quantile. For this reason Expected
Shortfall (also known as Conditional VaR or Expected Tail Loss) is often viewed as a more conclusive risk measure. ES can be defined as the expected loss given that the loss exceeds the equivalent VaR level. Unlike VaR, ES assigns equal weight to all quantiles greater than the specified Xth quantile.
The financial crises of 2007-08 sent shockwaves through banking systems globally, and many
U.S. and European institutions were hit with unforeseen losses. Many
References: Blanco, C., Oks, M. - “Backtesting VaR models: Quantitative and Qualitative Tests”. Danielsson, J. – “Financial Risk Forecasting”, 2011. Rachev, S.T., Stoyanov, S.V., Biglova, A., Fabozzi, F.J. - “An Empirical Examination of Daily Stock Return Distributions for U.S. Stocks”. Yamai, Y., Yoshiba, T. - “Comparative Analyses of Expected Shortfall and Value-at-Risk under Market Stress”.