On Float

[JBird]

Good discussion. I'd like to pose one more hypothetical.

 

$1 billion of cost-free float that must be paid back after 50 years is for sale. The float can only be invested in risk-free assets. The risk-free rate is 5%. Your required return rate / discount rate is 10%. What's the maximum amount you're willing to bid, and why?

87.2 m is the present value but you must account for inflation and sovereign risk. Probably something around 75m.

 

This example is in a sphere of unreality; so no inflation and no sovereign risk. I'm curious how you arrived at $87.2 million?

[constructive]

I assume the $1B float must be invested at 5%, but I can reinvest my equity in excess of that as I please. LC makes the opposite assumption.

 

So the float produces $50M risk free per year, and I require a 10% return. I will pay $500M.

[constructive]

I come up with $89.2M for the other calculation: $1B * 1.05 ^ 50 - $1B = $89.2M * 1.1 ^ 50

 

Close enough to $87.2M.

[LC]

Good discussion. I'd like to pose one more hypothetical.

 

$1 billion of cost-free float that must be paid back after 50 years is for sale. The float can only be invested in risk-free assets. The risk-free rate is 5%. Your required return rate / discount rate is 10%. What's the maximum amount you're willing to bid, and why?

87.2 m is the present value but you must account for inflation and sovereign risk. Probably something around 75m.

 

This example is in a sphere of unreality; so no inflation and no sovereign risk. I'm curious how you arrived at $87.2 million?

Wasn't thinking straight. That number is simply the present value of 1bln discounted at 5% over 50 yrs.

[JBird]

I assume the $1B float must be invested at 5%, but I can reinvest my equity in excess of that as I please. LC makes the opposite assumption.

 

So the float produces $50M risk free per year, and I require a 10% return. I will pay $500M.

 

Fantastic.

 

And finally, how far out can we project real-world float in the future and still stay within the bounds of conservatism? 20 years out? 50? 100? If it depends on the quality of the insurer, how far out can we go for the highest quality insurer's float?

[constructive]

To go from excellent (over 5% underwriting profit across the cycle) to average (5% underwriting loss across the cycle), for a large company like GEICO, I'd say 50 years. It's a punctuated equilibrium - the most dangerous points are when key people retire.

 

For a small company like Lancashire which is more dependent on key people I'd say 25 years.

 

What do you think?

[JBird]

I've been trying to think about this on a probability basis, using an expected value to answer the question of how far to project.

 

With a simple example, say we're looking to purchase $1 billion of float run-off that will last 1 year. We know the policy book. The question we have to ask is, how much float are we likely going to have throughout the year? It'll start with $1 billion but just how fast will it taper off? Absolutely nobody knows with precision how fast it will diminish. So we do all we can do; judge the probability of the different possible outcomes. For simplicity, say there are 2 possible outcomes, the first being that we have an average amount of $750 million, second being that we have $500 million. We estimate the odds are 60-40, respectively. So on a probability-weighted basis we'll have $650 million of float. Now it's only a matter of deciding what you're willing to pay for $650 million of float for 1 year.

 

I'm not suggesting this process be done with precision or that it must be laborious, but I think it may yield a useful answer.

 

My thesis is that you should project float out for as many years as you can judge the probability-weighted amount there will actually be.

 

Clearly this is easier when looking at an insurer like GEICO that has a strong competitive advantage. But if you're interested in projecting their float out 5 decades, what's your expected value for Year 40? Year 50? Those seem like a tough questions. Just consider how far away that really is. There are so many variables and unknowns. If we can't estimate the odds that far out, maybe it's safer not value those years. I'm not saying it's unconservative to value that far out, just that from my perspective it looks tough.