Aug 08

Value at Risk (VaR). 2007 FRM, Part 7: Cash Flow at Risk (CFaR)

by David Harper, CFA, FRM, CIPM

FRM | Risk |

cfar_intro

Learning Outcomes

  • LO 8.1: Calculate cash flow at risk for a firm with normally distributed cash flows for any period, given the expected return and volatility of firm value, and interpret the CFAR measure.
  • LO 8.2: Describe the characteristics of firms for which either VAR or CFAR is the more appropriate measure of risk.

Cash Flow at Risk (CFaR)

Cash Flow at Risk (CFaR) is close cousin to value at risk (VaR), appropriate to non-financial firms where cash flows are emphasized over asset values:

 

Metric

Statement Focus

In words

Value at Risk (VaR)

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Balance Sheet (stock)

 "We are 95% confident that the value of the portfolio/asset will not drop below $X, over then next year"

Cash Flow at Risk (CFaR)

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Cash Flow Statement (flow)

 "We are 95% confident that our firm's cash flow will not fall below $X, over the next year [because below $X is a shortfall]"

 

The formula is basically the same as VaR. It can be expressed as a dollar amount (e.g., we are x% confident that a cash flow shortfall will not occur over the next year) or as a percentage (e.g., assuming a shortfall occurs at $x million, we are x% confident that it won't happen, over the next year). In percentage terms:

cfar_basicformula

 

For example, assume our company's expected cash flow is $10 million with a volatility of $1 million. Further, assume we consider cash flow below $8 million to be a shortfall. Then we can say either:

  • Our 95% CFaR is $8.36 million: $10 million - ($1 million x 1.645) = $8.36 million. Or,
  • Our risk of shortfall is 2.275%. That's because $8 - $10 million = -$2 million. And $2 million below the expectation is - 2 standard deviations to left of mean. And =NORMSDIST(-2) = 2.275%. In English, the area to the left of -2 standard deviations is 2.275% of the total area under a normal distribution.

Which is appropriate, VaR or CFaR

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Value at Risk (VaR) Cash Flow at Risk (CFaR)
Primarily financial firms, because much depends on asset values Primarily non-financial firms, because much depends on cash flows
Firms that tend to fund growth by tapping capital markets Firms that tend to fund growth via internal cash flows

 

Of course, these categories are philosophical. I don't have data but I would assume a convergence and blurring of practices. Many financial firms have lately tended to increase their fee-based (flow-based) revenue streams, while conversely, many non-financial companies increasingly rely on balance-sheet based techniques that would suit VaR.

Takeaways

  • CFaR is an analogue to VaR: a probabilistic estimate that normally distributed cash flows won't fall below some level.
  • CFaR can be expressed as either: the probability that flows won't fall below some given level, or given a probability, the level at which flows won't fall below
  • VaR tends to suit financial firms who tap capital markets, CFaR tends to suit non-financial firms who grow internally. But these are gross simplifications. Most firms fall somewhere in between and increasingly adopt each others' practices.

Comments

  1. Jinxia Liu 21 Aug 2007

    hi David,I now consider something about CFaR.
    if i want to get CFaR of some industry, of which the firms has the similar capital,structure and so on , how can i think over ? thanks a lot

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