After buying Alternative Asset Opportunities (TLI) almost exactly one year ago I exited my position today at a very small loss (-2.4%). Fundamentally nothing really changed between today and one year ago. What changed was my understanding of the traded life interests. If you start with my oldest post on TLI and read the follow-up posts chronologically you see how with every update I realize that my model of the expected future cash flows needs to be refined, and obviously always in the ‘wrong’ direction. After my latest post on the fund I realized – with the help of a reader, thanks! – that the model was still too optimistic. With my perceived margin of safety evaporating the logical thing to do was selling my position.

I always write that readers should do their own research, and if TLI doesn’t prove the point I don’t know what will. I have compiled a quick list of all the things I missed initially:

• Update, Nov ’12: the average age of the portfolio doesn’t increase with one year/year.
• Update, Nov ’12: the ratio of females and males doesn’t remain constant
• Update, Oct ’13: added assumption that premiums increase 5%/year
• Update, Oct ’13: realization that some policies lapse when holder reaches age of 100
• Update, today: 5% premium increase per year too optimistic, probably 9~10%/year
• Update, today: reducing average age with one year doesn’t increase LE’s with one year

So keep this in mind the next time you read a post on my blog! Especially the last point in the list matters for the valuation. While quite obvious in hind sight I didn’t realize how big the difference was. If you assume that insured group is as healthy as a ‘normal’ 3 year younger group you only add 1 year to their LE. Given that the new LE provider is expecting that the insured group could have a LE that is two years above the previous estimates it’s now easy to see a scenario where you actually start losing money (and given the historical profile of policy maturities it certainly looks like they could be right). TLI simply doesn’t appear to be the opportunity I once thought it was.

Disclosure

No position in TLI.L anymore

Last year when I first wrote about Alternative Asset Opportunities (TLI.L) I was very enthusiastic since the fund promises to deliver high returns that are uncorrelated to the market since it invests in life insurance policies. I quickly realized that the estimated life expectancies were probably too optimistic, but that possible returns were still attractive. This week the fund released the final results for the fiscal year that ended 30 June 2013, so a good moment to check how the thesis is playing out so far.

Life expectancies

Last year wasn’t a very good year (for investors); the old guys and gals apparently didn’t feel like dying. The fund started the year with $166 million in face value of policies, and based on the average age of the insured (88.7 years) and the CDC 2008 life tables you would have expected that ~14% of the population wouldn’t survive the end of the year. The result didn’t come close to this number, and the few realized policies weren’t particularly large. An updated overview of the historical policy maturities, and the differences between the expected values and realized values is provided in the table below:

What’s also visible is that the fiscal year 2014 has a strong start, mainly thanks to one big $5 million policy that reached maturity. But at the same time it’s clear that the number of policies that mature is consistently lower than what would have been expected based on the CDC 2008 life tables. The annual report contains an excellent in-depth discussion about this issue, and the company has opted for a more conservative approach to estimate LE’s:

Up to the end of 2012, the Board obtained the majority of its LE estimates from two major providers. Although past experience is that they have tended to underestimate LEs, both have recently made alterations to their underwriting methodology to address these issues, and the Board was therefore keen to establish what, if any, effect these changes might have on the LEs previously provided. So it commenced a programme of re-assessment of LEs, involving 38 policies with a face value of well over half the total portfolio, and a total of 34 lives. So far, 29 of these policies have been fully re-assessed.

The Board was pleasantly surprised to note that the result of this exercise so far, if applied across the whole portfolio, would be to reduce portfolio LEs by approximately 1 month and increase valuations by around 1%. The Board has, however, become aware that third party evidence suggests that these providers continue to underestimate LEs, and this seems to correspond to the Company’s experience to date. LE estimates were therefore obtained, starting in April 2013, from a third provider, whose LE estimates typically are longer than those of other industry participants. As expected, their estimates for the policies assessed so far were indeed significantly longer (by an average of 24 months compared to the average from the original two LE providers).

Weighing this information up, the Board decided that it was appropriate to adopt the average of the three providers’ estimates, which take account not only of the most recent LE calculation methodologies but also of changes in the medical status of the insured lives. The use of a third LE provider introduces a more conservative element into the valuation process, although it should be noted that the majority of market participants have tended to use just the original two providers when trading policies. This new approach left two issues to be decided.

The first related to the valuation of those policies which have not recently (that is to say since 1 April 2013) had a new LE estimate. The Board could, of course, have continued its policy of using simply the last obtained LE estimate regardless of recency and providing projections for shareholders of the hypothetical effect of changes in LE for the remaining policies on the NAV. The Board has, however, decided that there is good enough evidence that it should use more conservative (i.e. longer) LEs, and that it cannot ignore the outcome of the figures obtained so far based on three providers. So far, 29 policies with a face value amounting to over 40% of the portfolio have been re-assessed. The average change in LE is an increase of approximately 12%.

I think that it’s probable that the new third party LE provider is closer to the mark with regard to the true life expectancies than the other LE providers. In my valuation I’m actually expecting that the average LE could be 3 years higher than the expectations from the CDC 2008 tables. While the company has adjusted their life expectancies upwards they are still slightly below the probabilities of the 2008 tables. I found this quote also interesting:

Past mortality is not, of course, a guide to future outcomes, especially as the LE basis has been changed, but if a continuing 50% mortality rate were to be assumed with an unchanged discount rate, the net asset value per share as at 30 June 2013 would have been 20.6p per share. This figure is provided to give shareholders a measure of the effect on the portfolio of low mortality rates, but it is an illustration only; in practice the high discount rate used in valuations at least partially allows for uncertainty in this respect.

Premiums paid

One thing that I missed in my initial valuation is that the company is apparently paying increasingly higher premiums. Last year the TLI paid $8.2 million in premiums (while expecting a $8.4 million bill) and it’s expecting to pay $8.7 million this year if there are no further policy maturities. So they are now paying more while they have a slightly lower amount of active policies. To account for this I have updated my model with the assumption that premiums for existing policies will increase with 5%/year.

The result of this new assumption is that the expected return drops from ~9% to ~7.5% at today’s share price. It’s certainly not a spectacular expected return, but given the low correlation with the market it’s still pretty good. And it should be noted that this is the expected return after assuming that the LE’s should be adjusted upwards by a full three years. I certainly think the LE’s of the company are too optimistic, but escaping death is getting pretty hard once you have a group of people with an average age of 89.6 years. Giving them a full three years higher LE than the general population might be overly generous, and if it’s in fact ‘just’ two years higher – in line with the expectations of the new LE provider – you are already looking at a 10% return.

Disclosure

Author is long Alternative Asset Opportunities (TLI.L)

While browsing the web I found an interesting blog post titled “Your body wasn’t built to last: a lesson from human mortality rates”. The fact that the average age of insured group in the TLI portfolio is going up is good news for investors. To quote the first part of the post:

What do you think are the odds that you will die during the next year? Try to put a number to it — 1 in 100? 1 in 10,000?  Whatever it is, it will be twice as large 8 years from now.

This startling fact was first noticed by the British actuary Benjamin Gompertz in 1825 and is now called the “Gompertz Law of human mortality.” Your probability of dying during a given year doubles every 8 years.  For me, a 25-year-old American, the probability of dying during the next year is a fairly miniscule 0.03% — about 1 in 3,000. When I’m 33 it will be about 1 in 1,500, when I’m 42 it will be about 1 in 750, and so on.  By the time I reach age 100 (and I do plan on it) the probability of living to 101 will only be about 50%. This is seriously fast growth — my mortality rate is increasing exponentially with age.

And if my mortality rate (the probability of dying during the next year, or during the next second, however you want to phrase it) is rising exponentially, that means that the probability of me surviving to a particular age is falling super-exponentially.

The next few months are also expected to be good for the TLI investor. Winter is the deadliest time of the year. A ‘fun’ graph from the @Legacy blog showing the daily deaths in the US indexed by month to January. The blue line shows the relative expected number of deaths while the red and green lines represent the 90% confidence interval.

It happens often that my understanding of a fund or a company changes materially after initiating my position, and Alternative Asset Opportunities is not an exception. But before I start with explaining how various of my assumptions have changed in this specific case I wonder if this phenomenon could indicate a flaw in my investing process. No new information has become available the past weeks, and everything discussed here is something I could have and probably should have figured out before entering my position. Doing the research before entering a position is in my opinion preferable because you risk that you become biased after making the decision to invest. On the other hand: it would also be stupid to stop researching your positions after entering them, and never changing your opinion on the appropriate valuation would also be troublesome indicator. So I haven’t yet really figured out how to think about this…

Historical performance

Anyway, to get back to TLI and life interests: a lot of people think that these products are more or less a black box where you have nothing to go on besides management projections and basic life expectancy information from the latest CDC tables. While this is true when the portfolio is assembled you get more and more information when the portfolio ages and you can compare realized maturities with expected maturities. If the face value of maturities runs consistently below the expected number it’s theoretically possible that it’s just bad luck and negative variance, but a more likely explanation is that the health of the insured group is better than expected and that the real life expectancy is higher that the estimated LE.

I have created an overview of the historical changes in the TLI portfolio in the table below and highlighted the most important rows. The first highlighted row shows how much money the fund collected from maturities while the second highlighted row shows how much you would have expected based on the average age of the insured group at the start of that year and the death probabilities for that age group as found in the CDC tables (using simple linear interpolation between probabilities if the age is not a round number). The numbers are not perfect because not all financial years have twelve months (made some simplistic adjustments for this as well) and policy sales also distort the picture (no adjustment for this).

There also seems to be some errors in the older annual reports. In 2008 one life policy was sold for $550K, but based on the reported face value of the policies at the start of the year and the number of maturities I get a face value of just 200K, and that obviously doesn’t make sense. The reported ending face value of the portfolio at the end of 2008 is reported as 243M which seems to be a copy and past error from the report from the previous year. It can’t remain constant if you have maturities in between. The numbers below aren’t perfect.

As is visible the amount of policy maturities have been running significantly below what would have been expected based on the CDC life tables. There could be bad luck in the equation here, but it seems quite unlikely to me that that is the full explanation. Guess the statistics nerd could figure out what the odds are of running this much below expected value, but I don’t think it can be a high number. Humans (I’m part of that group!) are however in a lot of cases pretty bad at estimating probabilities, so I probably should try to do the math. I’m hoping I have a reader that loves to solve these kinds of problems ;).

What my assumption would be is that while the insured group now has an average age of 89 their effective age is probably roughly three years lower. It’s not quite the same scenario though: what you would expect is that when the portfolio ages the effective age converges to the actual age. The results also seem to hint in this direction. The reason for this phenomenon is that the effect of a possible negative selection bias diminishes in time.

For example: lets say we have a population of 100 people that includes 10 people that have a life expectancy of 100 years at birth while the rest of the population has a 80 year LE. If you somehow manage to only buy the life insurance policies on this high LE group you make a massive mistake at earlier ages. But if you would do this when the average age of the population is 100 it could be that you have 5 people remaining that originally had a 100 year LE while maybe just one guy made it that originally had a 80 year LE. Now your sample is not that skewed anymore compared to the total population. This is obviously a bit theoretical and simplistic, but hopefully I managed to communicate the idea.

Modelling improvements

I have made two changes to the original valuation model: one minor, and one major. The minor change is to assume that an increasingly bigger part of the portfolio is going to contain females. This is because females have a higher life expectancy than males. In the table above you also see that the percentage of male lives in the portfolio is gradually dropping every year with the exception of 2012. This year the fund got a bit lucky with an equal number of male and female deaths. I’am assuming that every year the amount of male lives drops with 1.30 percentage points, in line with the trend between 2008 and 2011.

The bigger change is that the average age of the portfolio does not go up with one year every year. At first sight this seemed like a reasonable assumption, but this is not the case because not all persons in the portfolio have the same age. When the portfolio was assembled it contained policies on persons between the age of 78 and 92. What happens is that older persons have a higher probability of dying, slowing down the increase of the average age. This is also visible in the table above: you see that the average age has increased 3.4 years the last 4 years: the average age is going up 0.85 years/year.

I have created an updated Excel sheet where it is possible to change the variables discussed above. You can also change the discount rate to either figure out what the present value of TLI is today, or what IRR you can expect based on various share prices (download here).

The screenshot above (click on it for the full size version) shows that you should expect a 9% IRR if you think that the effective age of the insured group is three years lower than the actual average age. I think this is a pessimistic case because even if this adjustment is initially right it should shrink every year due to the earlier explained concept.

Conclusion

One of the reasons I try to buy investments at a large discount to my estimated fair value is to protect myself from mistakes in my own valuation. In the best case I’m completely right and make a lot of money, and if I’m not right it’s hopefully still undervalued. I think this is the case with TLI. Based on the historical maturities I think the effective age needs to be lowered significantly more than the -0.8 year adjustment used in the initial valuation, but I’am also fairly sure that the -3.0 adjustment is too pessimistic. What this implies is roughly a 10%+ expected return that is not correlated with the market. Still pretty awesome in today’s interest environment if you ask me.

And there is significant upside if the average LE as estimated by the fund is closer to reality than what you would assume based on the historical results. Given the huge gap between expected maturities and realized maturities some bad luck is probably at play. Important is that you don’t have to rely on this to get a good return. So I still like TLI a lot, but based on these new insights I do want to lower the ranking of this investment from the maximum five stars to four stars. The search for the elusive five star investment continues…

Disclosure

Author is long Alternative Asset Opportunities (TLI.L)

An investment that promises high returns and almost no correlation with the market? Wexboy seems to have found it in Alternative Asset Opportunities PCC Ltd. This is a closed-end fund listed on the London stock exchange that has investments in traded life interests (hence the TLI ticker). I suggest you start out with reading Wexboy’s write-up on the fund, aptly titled “An Investment To Die For” since he has all important points solidly covered and I’am not going to reinvent the wheel.

Present value

The question that I do want to answer is how much should should TLI be worth today? The fund is currently trading at 44.5 pence per share while NAV at 31 October, pro-forma adjusted for the equity issue earlier this month, was 56.0 pence per share. This is already a nice 20% discount, but I think the NAV is significantly understated because the company uses a ridiculous 12% discount rate to value their assets. While the capital asset pricing model (CAPM) does have it flaws the general idea behind it is solid: an investor should not be compensated for idiosyncratic risk because you can eliminate it using diversification. What matters is systematic risk.

So how much systematic risk does an investment in TLI have? You can probable argue that there are some relations between the life expectancy of 89 year old’s and the general economy, but it’s going to be far fetched. The only major source of systematic risk is the credit risk from the insurance companies that have underwritten the insurance policies. As a policy holder I imagine that you have a pretty solid position in the capital structure of these companies, but not to make things overly complicated: what happens if we use the yield on investment grade US corporate bonds as a discount rate? At the moment this yield is 3.3% according to Bloomberg, and using Wexboy’s spreadsheet, you can easily figure out expected cash flows. This gives me a present value of 89 million dollar (55.8 million pound) or 77.5 pence per share. This is still a reasonable conservative estimate in my opinion. Wexboy is nice enough to add almost a year to the average life expectancy of the old folks in his spreadsheet, and I think the proper discount rate is probably even closer to the risk-free rate (near zero these days…) than the yield of investment grade bonds.

Return of capital

I don’t expect that the market is going to agree with me on that discount rate anytime soon, but the good news is that the fund is basically in liquidation mode (shareholders actually have to vote every year to extend it’s life!) and intends to return all capital to shareholders. The fund already has the authority to buyback shares, and with all debt eliminated this month it shouldn’t take very long before they get enough cash to start buying back shares. Given the big discount between ‘true NAV’ and the current market valuation this could enhance returns even more.

Conclusion

I think that TLI offers a truly remarkable opportunity. The performance of the policies should have almost zero correlation with the market, and yet at the same time potential returns are very attractive. The biggest risk is that the insured group lives longer than expected, but with an average age of 89 and a 4.7 years weighted average LE you can’t be off by a huge amount. Not a lot of people manage to hit the magical 100 number, and there isn’t a lot of time for things to change radically. The life expectancy of a new born is much more uncertain.

Rating: just before the first anniversary of this blog I’m going to give out my first five star rating. I believe an investment in TLI is very low risk while the expected return is more than respectable. Not only is the risk/reward ratio great, there is a reliable catalyst: no-one can escape death…

Disclosure

Long Alternative Asset Opportunities, and looking to increase my position.