Hi,
Anyone can shed some light on the difference between shortfall risk and expected shortfall? shortfall risk is mentioned in the CFA III curriculum but only one brief line explanation is given. When I searched for this term on Google, most of the first few search results return “expected shortfall (or conditional VaR)”. I don’t think they are the same thing.
but then how to understand that the shortfall risk doesn’t indicate the magnitude of losses?
thank you!
Cheers
Liming
They are not the same thing.
Shortfall risk is the risk, given in percentage probability terms that an investment will end up below a specified level/return in a specified period of time. So for example if you invest £1000, there may be a shortfall risk of 10% that the investment will end up being worth £900 or less by the end of the specified investment period. The shortfall risk percentage gives no information as to the magnitude or “dollar amount” of losses to be expected if the investment does indeed fall below the specified amount. So in this example, if there is a 10% risk the investment will be worth less than £900, we still don’t have any information as to whether we can expect it to fall to £800, £700 or whatever if that 10% likelihood outcome comes to pass.
Expected shortfall (or conditional VaR) is a variation on VaR that tries to reveal information regarding average expected losses if the VaR level is actually breached. Regular VaR states a maximum amount in dollar terms that an investment/portfolio is likely to lose a certain % of the time, over a specified time period. So a 95% daily VaR figure of £1000 means that 95% of the time, the portfolio is expected to lose £1000 or less in one day. But if that level is breached, regular VaR gives no information as to the magnitude of loses we can expect…all we know is that it is “more than” £1000.
Expected shortfall tries to assign a dollar amount to these breaches of the VaR level, usually by taking an average of the losses that can be expected to occur the other 5% of the time (in a 95% VaR) and calling that “expected shortfall” or "conditional VaR, i.e. It is the dollar VaR amount we can expect to lose in a specified time period, a specified % of the time CONDITIONAL on the normal VaR level actually being breached.
I think the VaR is expressed the other way around?
5% VaR figure of £1000 means that 5% of the time, the portfolio is expected to lose more than £1000 in one day.
although what you say is equivalent, the graders might not think so.
Both ways of expressing it are exactly equivalent, section 5.2 Value at Risk, pg 153, Volume 5 states this point explicitly.
The authors do say that they “prefer” to state it as a minimum loss as “it is a bit more conservative, because it reminds us that the loss could be worse”.
But yeah, it can be expressed both ways. I actually usually express it as a minimum loss as you have, not sure why I chose to express it as a confidence level/maximum loss this particular time.