LaR vs. VaR (LaR < or > VaR) - K. Dowd

[emilioalzamora1]

Dear David,

I came across the following statement in Dowd's book:

'the LaR can be much greater than the VaR or much less than it, depending on the circumstances'

What does Dowd mean by 'depending on the circumstances' and are there any examples for narrowing down the term 'circumstances'?

The only example we have is the case where VaR < LaR when we have a (short-term exposure) of a LONG position in European-style options.

Can we otherwise say (in the light of 'depending on the circumstances') that if we have a SHORT position in European-style options, then VaR > LaR?

In short,

1.) VaR < LaR (for a LONG position in European-style options)
2.) VaR > LaR (for a SHORT position in European-style options)

And the other question what remains why is the short-term exposure of any relevance here?

Thank you!

 

[David Harper CFA FRM]

Hi @emilioalzamora1

The difference between LaR (aka, cash flow at risk) and VaR is analogous to the difference between asset value (at a point in time) and cash flow (over a period). Consider a long position in a 10-year bond, purchased at some discount to the face value. Value at risk measures the worst expected loss in value of the bond, which is a discounted value of future cash flows. Over the next one year horizon, say, there is some value at risk because rates can increase and the bond price can drop. However, over the next one year horizon, there is likely to be no cash flow at risk (as the long position does not have a worst expected outflow); or, the LaR could be defined in terms of the coupon cash flows expected, in which case there could be a risk of cash shortfall (if the bond defaults) relative to the coupons expected. But this is a fundamentally different perspective. Like VaR, LaR depends greatly on the definition (i.e., cash shorfall compared to what) such that greater than or less than rules in general are maybe not too helpful.

In the case of European options,

• long position: probably VaR > LaR, because the position can drop in value but in the short-run there is no cash flow risk to the holder
• short position: if the window is short-term, VaR may be also be > LaR because while the position can drop in mark-to-market value, the short will not be exposed to cash outflows (payments) until expiration. If the LaR horizon is less than the time to maturity, the short position may have no LaR during the measured horizon.

But in the case of American style options:

• long position: probably VaR > LaR (similar position)
• short position: now it's a different story. LaR may rival VaR as the position is exposed to a cash outflow

Dowd's chapter highlights the difference with a hedge, and his footnote Metallgesellschaft (MG) as a classic case study that highlights the difference between the value of a portfolio and the cash flow at risk. MG hedged long-term short positions with short-term long futures (stack and roll). In general, the hedge was somewhat effective such that, if it had been measured, MG's LaR was much greater than their VaR because short-run cash outflows were offset by long-term (yet unrealized gains). Cash flow losses on the hedge (the short-term futures) overwhelmed them, yet the net long-term value of their overall position was not actually very bad. So, in the context of cash flows (as reflected in LaR) versus mark-to-market value (as reflected in VaR), the time horizon can be the predominant factor. In many situations, over a long horizon, the LaR and VaR would necessarily converge because the mark-t0-market value ultimately discounts all the cash flows.

Here is Dowd (emphasis mine):

14.3 ESTIMATING LIQUIDITY AT RISK (LAR)
We turn now to liquidity at risk (LaR), sometimes also known as cash Flow at Risk (CFaR). LaR (or CFaR) relates to the risk attached to prospective cash flows over a defined horizon period, and can be defined in terms analogous to the VaR. Thus, the LaR is the maximum likely cash outflow over the horizon period at a specified confidence level: for example, the 1-day LaR at the 95% confidence level is the maximum likely cash outflow over the next day, at the 95% confidence level, and so on. A positive LaR means that the likely ‘worst’ outcome, from a cash flow perspective, is an outflow of cash; and a negative LaR means that the likely worst outcome is an inflow of cash. The LaR is the cash flow equivalent to the VaR, but whereas VaR deals with the risk of losses (or profits), LaR deals with the risk of cash outflows (or inflows).

These cash flow risks are quite different from the risks of liquidity-related losses. [footnote 11] Nonetheless, they are closely related to these latter risks, and we might use LaR analysis as an input to evaluate them. Indeed, the use of LaR for such purposes is an important liquidity management tool.

An important point to appreciate about LaR is that the amounts involved can be very different from the amounts involved with VaR. Suppose for the sake of illustration that we have a large market risk position that we hedge with a futures hedge of much the same amount. If the hedge is a good one, the basis or net risk remaining should be fairly small, and our VaR estimates should reflect that low basis risk and be relatively small themselves. However, the futures hedge leaves us exposed to the possibility of margin calls, and our exposure to margin calls will be related to the size of the futures position, which corresponds to the gross size of our original position. Thus, the VaR depends largely on the netted or hedged position, while the LaR depends on the larger gross position. If the hedge is a good one, the basis risk (or the VaR) will be low relative to the gross risk of the hedge position (or the LaR), and so the LaR can easily be an order of magnitude greater than the VaR. On the other hand, there are also many market risk positions that have positive VaR, but little or no cash flow risk (e.g., a portfolio of long European option positions, which generates no cash flows until the position is sold or the options expire), and in such cases the VaR will dwarf the LaR. So the LaR can be much greater than the VaR or much less than it, depending on the circumstances.

As we might expect, the LaR is potentially sensitive to any factors or activities, risky or otherwise, that might affect future cash flows. These include:

• Borrowing or lending, the impact of which on future cash flows is obvious.
• Margin requirements on market risk positions that are subject to daily marking-to-market.
• Collateral obligations, such as those on swaps, which can generate inflows or outflows of cash depending on the way the market moves. Collateral obligations can also change when counterparties like brokers alter them in response to changes in volatility, and collateral requirements on credit-sensitive positions (e.g., such as default-risky debt or credit derivatives) can change in response to credit events such as credit downgrades.
• Unexpected cash flows can be triggered by the exercise of options, including the exercise of convertibility features on convertible debt and call features on callable debt.
• Changes in risk management policy: for instance, a switch from a futures hedge to an options hedge can have a major impact on cash flow risks, because the futures position is subject to margin requirements and marking-to-market while a (long) option position is not.

Two other points are also worth emphasizing here. The first is that obligations to make cash payments often come at bad times for the firms concerned, because they are often triggered by bad events. The standard example is where a firm suffers a credit downgrade that leads to an increase in its funding costs, and yet this same event also triggers a higher collateral requirement on some existing (e.g., swap) position and so generates an obligation to make a cash payment. It is axiomatic in many markets that firms get hit when they are most vulnerable. The second point is that positions that might be similar from a market risk perspective (e.g., such as a futures hedge and an options hedge) might have very different cash flow risks. The difference in cash flow risks arises, not so much because of differences in market risk characteristics, but because the positions have different credit risk characteristics, and it is the measures taken to manage the credit risk – the margin and collateral requirements, etc. – that generate the differences in cash flow risks.

footnote 11: 11 The link between cash flow risks and risks of loss associated with cash flow risks is important, and anyone who has any doubts on this needs to re-examine the Metallgesellschaft debacle of 1993. In the early 1990s, a US subsidiary of MG, MG Refining and Marketing, had sold a large number of long-term guarantees on the oil price, and it hedged the resulting oil price risk using futures and swaps. However, when oil prices fell in 1993, its hedge positions lost a lot of value, and MGRM faced large margin and collateral calls on them. These created a huge cash flow drain, and the firm ended up making a loss of about $1.3bn. The MG case shows very clearly that cash flow problems can easily lead to ‘real’ losses – and potentially very large ones too.