# how to calculate the cost of float?

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Hi there, looking for some help.  I've been studying the way Buffett calculates the cost of float in his letters, and it seems wrong to me.  This is the formula he uses:

"cost of float" = (underwriting profit or loss)/ (net loss reserves + loss adjustment reserves + funds held under reinsurance assumed - agents balances - prepaid acquisition costs - prepaid taxes - deferred charges applicable to assumed reinsurance)

The problem is that what you are really interested in is the total cost of a policyholder relative to premiums paid by that policyholder.  In the case of a "steady-state" insurer (one where premiums received and claims paid out are both relatively constant over time) you can calculate that cost on a population basis.  I did a little simulation ("constant float") of what that would look like for a hypothetical group of policyholders that each pays in at the start of year 1 and makes a claim for the same amount at the start of year 5.  As expected, this generates a constant level of float so long as inflows and outflows remain constant.  Note that the cost of float is zero in steady-state - again as expected.  Notice also that the float appears unusually cheap (so much so that you're getting paid to hold it) until the "tail" begins (the longer the tail, the longer the period of apparently low-cost float).

Now the interesting case is where the insurer never reaches steady state because premiums grow each year ("diverging float").  This is the case at Berkshire.  Note that in this case float is costless for as long as the premiums continue to grow.  Notice this has nothing to do with the quality of the underlying underwriting and everything to do with an ever-increasing supply of fresh premiums that haven't yet hit tail.

The final case is one of declining premium volume - a point that most aging insurers will reach sooner or later.  In this case float appears very expensive for the entire period using Buffett's formula - although the underlying underwriting quality was identical.

Hopefully you understand my concern now.  The calculation Buffett does makes float look great even with poor underwriting so long as the premium growth continues.  But there would conceivably come a point where - as premium growth inevitably slows - that poor underwriting would start to manifest as an increasing cost of float.  And by the time Berkshire reached steady-state float, they'd be contending with extremely high-cost capital that they couldn't give back.

I worry that catalysts could be reduced compounding in float and book in future years - a certainty.  Buffett made some serious underwriting screwups in the 70s and I worry that this a uniquely long-tail diagnostic issue.  Float is - after all - still leverage, and leverage always has a downside.

cost_of_float.xlsx

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Trying to work out your concern.

You seem to assume that you get a costless growth of float as long as premiums grow.

Cost of float and float growth are not directly related.

Cost of float is a function of the net underwriting result for the year and float growth will tend to reflect the balance between net premiums growth and declining premiums in run-off based on the trend of the last few years.

A P+C firm can report relatively minor underwriting losses (CR less than 100%) and report an underwriting gain (so negative cost of float) while at the same decreasing float (soft market, firm walking away from market share).

In 2017, for instance, BH reported an adverse development cover on the AIG transaction (which will tend to increase the cost of float for that year) while, at the time, the transaction contributed to a very significant growth in float.

You may find the following link interesting (look Table 3, page 39):

BTW, I don't agree with the author's main conclusions but the article contains valuable information.

BH has grown float at very significant rate, especially in the early years but it was, at times, far from costless (but still, in general, less than the other traditional sources of financing).

I would submit that "poor underwriting" does not fit with the underwriting profile reported in the last few years.

In the 2017 report, Mr. Buffett describes a relative steady state in terms of the growth of float but suspect that he is aiming for continued profitable underwriting.

The whole thing about the valuation aspect of float assumes that the firm is a going concern. Once in run-off, by definition, the combined ratio loses some of its significance and float is no longer expected to be a permanent feature of the capital structure (different economics). In run-off, there's no Ponzi scheme if sufficient reserves have been put aside.

I would add also that, irrespective of investment income obtained from float, the reported combined ratio tends to overestimate the cost of float as the loss reserve expenses are not discounted and that component may be significant in long-tail lines.

Hope that helps.

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Also insurers have inflation on their side. New business is coming in at higher prices than old policies (and claim against) were written.

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Agree that inflation would help to validate premium price increases but the net result may not be so clear cut.

On the underwriting side,

-claims reserves and premium prices are generally set with the assumption that average inflation rates are simply imbedded in the experience and projected to continue. Rising inflation will result in insufficient reserves, especially for long tail lines. Rising rates for premiums would try to reflect new inflation rates and some price increases may be pushed to catch-up or compensate for previously inadequate rates but that introduces an uncomfortable level of uncertainty.

-claim cost development (inflation) may vary across different lines and across many dimensions that were not factored in at the underwriting phase and that may end up much higher than CPI: medical costs, "social" cost trends (litigation trends etc) and workers' compensation costs in general.

Inflation is an historical fact for some of us but for some people in the insurance business in the 1970's, despite some mitigating contract features, it seemed to be a big deal on the operational side.

For those interested, seminal work (work by Mr. Masterton):

On the investment side,

Mr. Buffett wrote his classic article on the swindling role of inflation on investments in the 70's and, even if investment float is considered to be a somewhat "natural" hedge on inflation, rapidly rising inflation would tend to have net adverse effects for some time on the investment portfolios of P+C insurers and reinsurers.

Interestingly, in 2011, Martin Sullivan, ex-chief executive of AIG, said that inflation may be the biggest risk ("the monster under the bed") although one may take the clairvoyance with a grain of salt since he had previously admitted that "he knew virtually nothing about the insurance company's vast exposure to complex financial insurance products until the credit crunch sparked early signs of a meltdown at the near bankrupt firm." ::)

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One other factor that should be considered imo is the equity used to support the float.

If you don't think that's a real cost just call up your states insurance regulator and say you want to write \$1 BB in P&C policies and since you expect a positive underwriting ratio you don't want to put up any equity...

I think the cost of float probably needs to account for the cost of any equity being held in lower risk lower return vehicles that supports the float. I'd suggest something like equity required × (cost of equity - risk free rate) needs to get added to the cost.

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"I think the cost of float probably needs to account for the cost of any equity being held in lower risk lower return vehicles that supports the float. I'd suggest something like equity required × (cost of equity - risk free rate) needs to get added to the cost."

Interesting concept but I'm not sure I follow.

Are you suggesting to integrate the cost of equity into the cost of float to make it a firm-wide cost of capital measure?

Are you saying the role of equity capital (excess or surplus capital) is to be invested in fixed income as a sort of "reserve"?

Here's my take (perspective):

-I see cost of float more as an operational measure not related to an opportunity cost.

-most insurance firms (even BH, for the most part, especially recently and for the insurance capital section) try to match insurance reserves liabilities to float assets by investing in a matched-duration cash and fixed income portfolio.

-there is more variation for the equity (or excess capital, surplus) part but this is the area where firms tend to use more discretion for more "risky" exposures. Markel, for instance, aims 80% exposure of equity or surplus capital to market equities.

-my understanding is that regulators show more flexibility, in terms of investment guidelines, for excess or equity capital.

Maybe a notion that helps to bridge with your perspective is that the return on capital for most P+C firms has been relatively disappointing for quite some time and this may be related to the fact that the cost of float continues to be underestimated by most (especially from a complete underwriting cycle point of view). An explanation could be that there is simply a surplus of capital in the aggregate.

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You seem to assume that you get a costless growth of float as long as premiums grow.

Cost of float and float growth are not directly related.

Cost of float is a function of the net underwriting result for the year and float growth will tend to reflect the balance between net premiums growth and declining premiums in run-off based on the trend of the last few years.

A P+C firm can report relatively minor underwriting losses (CR less than 100%) and report an underwriting gain (so negative cost of float) while at the same decreasing float (soft market, firm walking away from market share).

It seems like cost of float and float growth are related under Buffett's definition, although I agree that it would be much more desirable for them not to be.  I assumed in the model that each policyholder will ultimately collect exactly what they pay in, which would make for a combined ratio of 100%, ignoring operating costs and inflation, on a per-policy basis.

I agree with your definition of "cost of float" as better than Buffett's - but coming up with an actual formula is difficult for an insurer that is not in steady-state.  You have to somehow link together the premiums collected for a book of business with the claims that book ultimately generates.  In a heterogeneous policy pool (e.g. auto claims, supercat, etc) the average-time-to-claim would vary dramatically so you would have to segment those books somehow also.

I'm a bit confused on your 3rd point - wouldn't a CR < 100% by definition be an underwriting gain?  The converse wouldn't be true - you could have CR > 100% and have an underwriting gain but operating costs out of control.  To the broader point though, you're right that underwriting can be profitable or unprofitable, and highly profitable underwriting would counteract the premium growth variable.  But unless underwriting quality varies dramatically, the simulation seems to suggest that there would be situations where premium growth would be the dominant variable using Buffett's formula.

Buffett has this kind of schizoid thing going on where he talks about how long-tail business will by definition feel artificially profitable for many years - and that tendency just worsens when the ratio of fresh/ seasoned business is high (effectively you partly reset the clock each year).  But in the next paragraph he typically goes on to say that their cost of capital is lower than the government's - even though the cost of debt is fixed upfront and can only go down from today's levels due to inflation (it wasn't always like that, but he's been saying this since the mid-90s when rates were already on the decline).  With float, the cost of capital rises with inflation because you don't get to fix your cost of capital upfront the way the government does (talking about seasoned vs newly issued bonds).  I think Buffett got an artificial sense of the attractiveness of float since rates have generally fallen between 1980-present, similar to how he said in the late 90s that stocks were not overvalued if interest rates remained low.  I think this perception could change dramatically over the next 40 years.  I still think the premium growth factor is more important than the inflation factor under most circumstances, but inflation looks like a second secular factor that could work against Berkshire's model (or Fairfax for that matter).

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One other factor that should be considered imo is the equity used to support the float.

If you don't think that's a real cost just call up your states insurance regulator and say you want to write \$1 BB in P&C policies and since you expect a positive underwriting ratio you don't want to put up any equity...

I think the cost of float probably needs to account for the cost of any equity being held in lower risk lower return vehicles that supports the float. I'd suggest something like equity required × (cost of equity - risk free rate) needs to get added to the cost.

That's an interest point.  If you count just what is in the insurance businesses I guess the equity is 258B (cash and investments) - 114B (float) - X (other liabilities)?  I'm also not sure what you would pick for the cost of equity.

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One other factor that should be considered imo is the equity used to support the float.

If you don't think that's a real cost just call up your states insurance regulator and say you want to write \$1 BB in P&C policies and since you expect a positive underwriting ratio you don't want to put up any equity...

I think the cost of float probably needs to account for the cost of any equity being held in lower risk lower return vehicles that supports the float. I'd suggest something like equity required × (cost of equity - risk free rate) needs to get added to the cost.

I'm not a CAPM guy, although you could go that way.

I'd probably use what I think their equity portfolio will return over a long period of time, ~8-10% or so.

That's an interest point.  If you count just what is in the insurance businesses I guess the equity is 258B (cash and investments) - 114B (float) - X (other liabilities)?  I'm also not sure what you would pick for the cost of equity.

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"I think the cost of float probably needs to account for the cost of any equity being held in lower risk lower return vehicles that supports the float. I'd suggest something like equity required × (cost of equity - risk free rate) needs to get added to the cost."

Interesting concept but I'm not sure I follow.

Are you suggesting to integrate the cost of equity into the cost of float to make it a firm-wide cost of capital measure?

Are you saying the role of equity capital (excess or surplus capital) is to be invested in fixed income as a sort of "reserve"?

Here's my take (perspective):

-I see cost of float more as an operational measure not related to an opportunity cost.

-most insurance firms (even BH, for the most part, especially recently and for the insurance capital section) try to match insurance reserves liabilities to float assets by investing in a matched-duration cash and fixed income portfolio.

-there is more variation for the equity (or excess capital, surplus) part but this is the area where firms tend to use more discretion for more "risky" exposures. Markel, for instance, aims 80% exposure of equity or surplus capital to market equities.

-my understanding is that regulators show more flexibility, in terms of investment guidelines, for excess or equity capital.

Maybe a notion that helps to bridge with your perspective is that the return on capital for most P+C firms has been relatively disappointing for quite some time and this may be related to the fact that the cost of float continues to be underestimated by most (especially from a complete underwriting cycle point of view). An explanation could be that there is simply a surplus of capital in the aggregate.

Not a firm wide measure for BH, more like insurance subsidiary wide. I'm not totally sure how to calculate it, and I just thought of this idea while I was reading the thread, so I don't have it totally fleshed out. I think it is fair to say that BH carries more cash and bonds than it otherwise would if it didn't write a bunch of insurance. To the extent that any of that is funded by equity, suboptimal returns on that equity should be included when valuing the float, imo, because those suboptimal returns are part of the cost of using that float.

I was thinking about it more on a theoretical level, and BH may have enough equity in subsidiaries that they are only using float to fund the cash/bonds necessary to run an insurance subsidiary.

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"I think it is fair to say that BH carries more cash and bonds than it otherwise would if it didn't write a bunch of insurance. To the extent that any of that is funded by equity, suboptimal returns on that equity should be included when valuing the float, imo, because those suboptimal returns are part of the cost of using that float."

Let's take this further.

-BH is unusual in the sense that it is made of many components and one of the components (main one) is the insurance business.

-Financial instruments are fungible so this topic is more conceptual in nature.

Not to focus on semantics but I would suggest that float is not funded, as it accumulates in the normal course of operations. Think of this as a component with a the new label of "long term insurance working captal" assets (float) and matching liabilies (reserves). It just builds over time. I see the equity (or multiple sources of equity for BH) as a cushion that needs to be financed or funded. Even if you consider a newly formed insurance firm, the funding part to start operations would be temporary as float assets would accumulate in parallel to reserves and allow these initial funds to be given back to owners.

How the owner/CEO manages (allocation) the float is the fascinating question. In reply #1 above, I referred to an article (Buffett's alpha) which implies that a significant part of the magic was that Mr. Buffett "simply" used float as cheap leverage in order to buy cheap and safe equities.

What's the evidence. Early on, that may have been true to some extent. Not so much since 1995, it seems.

These are not GAAP numbers but the table clearly shows that Mr. Buffett has essentially matched insurance reserves with a "float" portfolio of cash and fixed income. One could say that he may have dipped in the float portfolio to some degree when faced with cyclical opportunities ("coverage ratio" going slightly below 100% in periods where stock prices were decreasing faster than GDP). But I suggest that float has not been "funded" by equity.

I submit that the above allocation concept can be generalized to many or most insurance companies although the end result is rarely if ever as satisfacory in comparison to what Mr. Buffett has accomplished.

Again, maybe a way to reconcile the perspectives is that the cost of equity of an insurance company needs to reflect the fact that it is effectively a leveraged structure (in the sense that there is a risk the corresponding assets and liabilities won't match) even if the capital structure has no true debt.

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Thanks cigarbutt! I agree BH is a special case, as for most insurers I think looking at the firm wide roe would suffice.

That table in the link is a great one, as it indicates that float and cash/bonds have been roughly equal. If you assume the float funds the least risky assets, that means equity is nearly all invested in equities and subsidiaries, aside from a small cash buffer that the operating businesses probably need. I agree money is fungible, but do think it makes sense to mentally assign the float to the lowest risk assets since it is money that the firm is holding for its clients.

So while I still think a theoretical adjustment makes sense, given the facts it isn't necessary for BH, imo.

That might be one of the advantages of the BH structure, as I suspect given their balance sheet strength they get more leeway on cash balances than others might.

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