# Shortfall risk vs Value at risk

Hi,

So can anyone differntiate between the two risk measures ? as far as I know, **shortfall risk** gives the probability of the return from the portfolio falling below the speciifed minimum target return while **VALUE AT RISK **is the probability of a portfolio losses go lower than a specfied amount at specfied period?

Both do not provide the extend at which lossses or return can be lower than a specifed ammount right? Both also does not measure the lossess in dollar ammount right?

IS the differece only return vs losses here or what?

Thanks

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Shortfall risk is the risk of experiencing a shortfall and is a percentage.

VAR is the maximum possible loss in a set period of time and would be a dollar amount.

minimum

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It is in their names…

Shortfall- “falling short” of target/min. return., so you are looking for a probability.

Value-at-risk- “value”/ how much money is at risk. 5% VAR, the worst 5% would be incurring losses at least a certain amount.

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Thank you onlysimon

you will also see shortfall risk being expressed in terms of number of standard deviations from the mean.

examples

1. “Webb suggests that their portfolio be structured to limit shortfall risk (defined as expected total return minus two standard deviations) to no lower than a negative 12 percent return in any one year.”

Book 2 (Institute 213)

2. “Another kind of ALM risk objective relates to shortfall risk with respect to plan liabilities. (Shortfall risk is the risk that portfolio value will fall below some minimum acceptable level over some time horizon; it can be stated as a prob- ability.) Shortfall risk may relate to achieving:

■ a funded status of 100 percent (or some other level) with respect to the ABO, PBO, or total future liability;”

Book 2 (Institute 439)

3. “Still another way for an investor to quantify risk is in terms of shortfall risk, the risk that a portfolio’s value will fall below some minimum acceptable level during a stated time horizon. The risks that a retiree’s assets will fall below the amount needed to supply an adequate retirement income, or that a defined-benefit plan’s assets will be less than the present value of plan liabilities, are examples of shortfall risk. When shortfall risk is an important concern for an investor, an appropriate shortfall risk objective improves the description of the investor’s attitude to risk. Shortfall risk is one example of the larger concept of downside risk (risk relating to losses or worse than expected outcomes only). Downside risk concepts include not only shortfall risk but concepts such as semivariance and target semivariance that also may be applied in asset allocation and are discussed in statistical textbooks (as well as defined in the glossary). The oldest shortfall risk criterion is Roy’s safety-first criterion. Roy’s safety-first criterion states that the optimal portfolio minimizes the probability over a stated time horizon that portfolio return, RP, will fall below some threshold level RL that the investor insists on meeting or exceeding. The safety-first optimal portfolio maximizes the safety-first ratio (SFRatio):”

Book 3 (Institute 192)

Institute, CFA. CFA Institute Level III 2014 Volume 3 Capital Market Expectations, Market Valuation, and Asset Allocation. Wiley Global Finance, 2013-07-12. VitalBook file.

CP

From the EOC answers … commentary which is useful

“One of the shortcomings of shortfall risk is that it is not as commonly used as standard deviation, and there is relatively less familiarity with shortfall risk. Also, its statistical properties are not well known. Unlike VAR, it does not take the form of a dollar amount. Finally, the shortfall risk gives the probability of the returns from the portfolio falling below the specified mini- mum target return, but it does not provide any information about the extent to which the return may be below the specified minimum target.”

CP

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Ok thanks guys,

So the conclusion is that VAR does express the loss in dollars ammount, but it does not provide the extent of how far losses can go. Shortfall risk is indeed does not provide the losses in dollars amount, and it does not provide how far the losses can go too.

correct me if I am worng.

what I’m confused with, is that those same EOC answers say

“Because shortfall risk is not based on normality assumption, it may be used as a risk measure” (for bonds with embedded options)

Yet it uses standard deviation, which is a normal distribution measure, no?? I’m so lost here. A. does it or does it not use standard deviation in it’s calculation? and B. why then is it ok to use shortfall risk for embedded options, but we should be cautious using Sharpe ratios, etc.

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Which vol/los/rdg’s eoc?

Reading 22, FI Port Management, EOC #1

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I guess this distinction has to do with min acceptable return (mar)

typical normality assumption requires to consider all outcomes to measure probability.

in this case, your set of outcomes are only those that exceed mar. Similar to returns with embedded options where no negative returns is the assumption. Therefore shortfall risk might violate normality assumption.

however, I’m not sure how portfolio with embedded option (written call option) would relate to min acceptable return situation

i could hv made this up. Pls comment

Shortfall risk does not require normality. It does however require a description of a return distribution. It can be any type of distribution as long as it can be integrated. If you have that, then all that is needed is a target return. The confusion may come when dealing with Roy’s Safety First Criterion. Roy’s is an application of shortfall risk to the normal distribution.