Obamacare 5 years later. Crow, anyone?

[sunmaster14]

It's not quite the same, in that there aren't offsetting risks in terms of insurance.

When you're talking about portfolio diversification, you're relying on the fact that each individual investment has risk, but that the variance in their risks respond to different economic levers. When the cost of sugar cane is high, people buy more corn to compensate. The two crops grow in different climates, and are very rarely affected by the same weather phenomena. So the risk of having a bad cane year is offset by the corn investment. They move in different directions.

This doesn't really happen in health insurance. Risks don't really offset. There are risks of global things, like pandemics, but they affect everyone - there's nobody who gets healthier when there's a pandemic. There's some shifting of where a service occurs - for example, between ER and Urgent Care, or between Inpatient Hospital and Long Term Nursing.

But the inherent risks of the people involved don't offset each other. There's no group of people that get healthier when a different group gets sicker. So from that perspective, the diversification perspective really doesn't work at all.

Generally speaking, we pool risks because it makes them more predictable. Health insurance is a compound distribution. Both the frequency and the severity distributions are extremely long-tailed. The smaller the number of covered lives, the larger an impact the variance has to actual experience. When we pool a larger number of risks together, it might result in an overall higher mean (the expected cost that drives premium), but it reduces the variance.

It's also a bit of a value at risk problem, in that IF something on the tail occurs, it has a much larger impact on the experience of a small pool than a large pool.

I was composing an answer, but I see that Francesca did it for me. I agree with everything she wrote. There's actually quite a bit of systematic risk in investment portfolios which is not possibly to diversify away without sacrificing yield (i.e. shorting assets with positive yield). I doubt there is any systematic risk in health care insurance aside from general increases in costs (which don't change much year to year), new government regulations (which also don't change much from year to year), and pandemics.

 

[Emily's Cat]

I am absolutely sucking at expressing this.

With investments, someone might look at your portfolio and say "Overseas investments historically perform very well and had high returns... but you have too many of them. You need to add some domestic investments to mitigate the risk in those oversease investments."

With insurance risk pooling, nobody every says "Healthy people have historically performed well and had low costs... but you have too many of them. You need to add some sick people to mitigate the risk in those healthy people."

ETA: Also, nobody ever says "Sick people have historically performed well and had low costs... "

It doesn't work. So how do I express that?

 

[Francesca R]

Except that in diversification, the whole point is that some of the variances are negatively correlated.

No it isn't. Negative correlations with positive expected returns are rare. They are great (I love them) but they are not necessary. Your investopedia link is consistent with this. (I know you're a health actuary but I'm a portfolio manager and have been in asset management for 19 years)

The result from diversification is that the overall mean return is higher and the overall risk is lower than for the individual investments in the portfolio.

The mean return isn't higher. It can't possibly be higher than the return of every component asset if you give that a minute of thought (it is the average). Diversification is only about lowering risk, which is standard deviation, variance or the second moment of return. And it is possible for the portfolio risk to be lower than the risks of many of the individual assets. (Potentially all of them)

In health insurance risk pooling, it's reasonable to assume independence of the "investments" - the investments are all independent people.

Not independence in the sense of zero correlation, as above, just less than 1. almost everyone gets sick eventually, and nobody has "negative costs"

I'm expressing this poorly. Adding more lives into the pool doesn't materially reduce the variance of the compound distribution... it just smooths out the tail.

It does until the lower limit is reached. And you wrote that it did reduce the variance a few posts up.

 

[Emily's Cat]

No it isn't. Negative correlations with positive expected returns are rare. They are great (I love them) but they are not necessary. Your investopedia link is consistent with this. (I know you're a health actuary but I'm a portfolio manager and have been in asset management for 19 years)

The mean return isn't higher. It can't possibly be higher than the return of every component asset if you give that a minute of thought (it is the average). Diversification is only about lowering risk, which is standard deviation, variance or the second moment of return. And it is possible for the portfolio risk to be lower than the risks of many of the individual assets. (Potentially all of them)

Okay - I don't know all that much about investments, outside of what I learned for my exams.

Not independence in the sense of zero correlation, as above, just less than 1. almost everyone gets sick eventually, and nobody has "negative costs"

I do mean independence in the sense of zero correlation. Or at least very, very near zero. As I said - pandemics, hurricanes, those sorts of catastrophic events affect the whole population, so not perfectly zero. But very, very, very near zero.

It does until the lower limit is reached. And you wrote that it did reduce the variance a few posts up.

I don't know what that means. I know I wrote that it lowers the variance... but I'm having a hard time translating what happens into the right terms. There's a gap between my statistician and my actuary brains, and my statistician brain is not necessarily up to spec.

Regarding the bolded bit above:
"And it is possible for the portfolio risk to be lower than the risks of many of the individual assets. (Potentially all of them)"

I think part of my problem expressing this is that I keep mish-mashing terms. So I'll be explicit: The "risk" in my context is 1) the risk of an individual person experiencing many claims and/or 2) the risk of the cost of the claim being large. There are "risk" elements associated with both the frequency and the severity distributions. At the end of the day, it translates to the risk of the aggregate annual claims being large.

ETA: It's the risk that either E(N) is large, or E(S) is large, or E(N)*E(S) is large

Here's where I'm getting stuck in this.

My understanding is that for investments, no matter where you start out, if you add MORE investments to your portfolio, then the risk of a low return will reduce - the more you add, the lower your risk of a lower-than-systemic return. Given enough investments, you can essentially diversify away all of the independent risks and get very, very close to the underlying systemic market risk.

Is my understanding correct? It's been a while, so it's possible I'm way off the mark.

Assuming my understanding is correct... is it possible to start with a set of "good" risk investments, and add more investments in such a fashion that the risk is higher than it was in the beginning?

In health insurance, adding more people doesn't necessarily lower your risk of having high annual claims. It's possible to select a smaller number of people, and experience a lower risk of high claims than you would if you had a larger number of people.

What I *think* is going on is that not everyone has the same risk of high claims (different levels of health), and also each person's risk of high claims is essentially independent of the risk of other people (in the sense of near-zero correlation).

 

[Nihilianth]

LOL. Because without the americans, the world would fall to shambles, right?

I think you just won the thread.

 

[sunmaster14]

<snip>

My understanding is that for investments, no matter where you start out, if you add MORE investments to your portfolio, then the risk of a low return will reduce - the more you add, the lower your risk of a lower-than-systemic return. Given enough investments, you can essentially diversify away all of the independent risks and get very, very close to the underlying systemic market risk.

Investment managers call risk volatility, which is the standard deviation in returns around the expected or mean return. If you have one big investment in, say, Google stock, your volatility will be equal to that of Google stock, which is about 23% per annum as implied by the options market. If you replace half of your Google investment with another stock, say ExxonMobil which has lower volatility than Google (16% per annum implied, to be precise), then your portfolio volatility will be reduced, regardless of the correlation between XOM and GOOGL. If you replace it with an investment that has higher volatility, say Facebook, which has 32% implied vol, then you may have actually increased the volatility of your portfolio. Or reduced it. It depends on the correlation between GOOGL and FB. Actually, I get the volatility is reduced if the correlation is less than 0.4 and is increased if the correlation is greater than 0.4. The formula is sqrt(S₁²/4 + S₂²/4 + rho*S₁*S₂/2), where S₁ and S₂ are the standard deviations of the individual stock returns (i.e. volatilities), and rho is the correlation coefficient.

Is my understanding correct? It's been a while, so it's possible I'm way off the mark.

Not wholly correct, but not wholly off the mark either.

Assuming my understanding is correct... is it possible to start with a set of "good" risk investments, and add more investments in such a fashion that the risk is higher than it was in the beginning?

Yes, of course, but it requires adding investments with a higher volatility than the current portfolio risk and a high enough correlation to the current portfolio.

In health insurance, adding more people doesn't necessarily lower your risk of having high annual claims. It's possible to select a smaller number of people, and experience a lower risk of high claims than you would if you had a larger number of people.

I really think the analogy with investment portfolios is perfect. The case of health insurance is simpler, though, because the correlations are pretty much zero. Therefore, you gain a lot of risk reduction by combining people into larger pools and insuring the whole pool. But if you add higher risk people, you can make the pool riskier, in theory. Note that what I call risk has nothing to with expected expenses. That is an entirely different thing, although it may be true, even likely, that somebody with high expected expenses has higher volatility too. In theory, it's possible for somebody to have high expected expenses (for treatment of a chronic disease, say), but low risk because their expenses are very predictable and don't change from year to year. As long as you are charging people premiums equal to their expected expenses, then their level of expenses is irrelevant.

What I *think* is going on is that not everyone has the same risk of high claims (different levels of health), and also each person's risk of high claims is essentially independent of the risk of other people (in the sense of near-zero correlation).

Once again, don't confuse high expected claims with risk. I agree with the expectation that there is near-zero correlation in claims between different people, however. Only a pandemic could make the correlation materially different from zero.

 

[sunmaster14]

I think you just won the thread.

Making an inane and gratuitous comment about a subject which is off-topic wins the thread? Ummm, ..., no.

 

[Nihilianth]

Making an inane and gratuitous comment about a subject which is off-topic wins the thread? Ummm, ..., no.

It wasn't off-topic. "American Exceptionalism," right?

 

[Emily's Cat]

Thanks for the run down - that is helping me see where I've gone sideways.

I really think the analogy with investment portfolios is perfect. The case of health insurance is simpler, though, because the correlations are pretty much zero. Therefore, you gain a lot of risk reduction by combining people into larger pools and insuring the whole pool. But if you add higher risk people, you can make the pool riskier, in theory. Note that what I call risk has nothing to with expected expenses. That is an entirely different thing, although it may be true, even likely, that somebody with high expected expenses has higher volatility too. In theory, it's possible for somebody to have high expected expenses (for treatment of a chronic disease, say), but low risk because their expenses are very predictable and don't change from year to year. As long as you are charging people premiums equal to their expected expenses, then their level of expenses is irrelevant.



Once again, don't confuse high expected claims with risk. I agree with the expectation that there is near-zero correlation in claims between different people, however. Only a pandemic could make the correlation materially different from zero.

Okay... In the sense of just plain old variance of the distribution, yes, adding more people will make the aggregate variance lower.

But it doesn't reduce the claim level... and it doesn't reduce the risk of experiencing a catastrophic-level claim. I don't know how to make that item parallel the investment analogy.

Lets say I've got a nice happy pool of people, and I add a hemophiliac.

The likelihood that they make a claim is higher than for the other people in the pool - Their E(N) is higher. The likelihood that their claims are very expensive, given that one occurs, is also higher - Their E(S) is higher. The long left end of the tail is also fatter for a hemophiliac - that is, there's a higher likelihood of them being further out on the tail, and the chances of them having a claims that is more than 2 standard deviations away from the mean is also higher. So that would mean that this person's severity variance is higher, right?

When I talk about risk, in my bailiwick, it's generally a combination of E(N)E(S) and V(S). I *think* it's more analogous to VaR, but not so well defined.

A hemophiliac is a "high risk" policy holder. There's a much higher chance of them having very high claims than other people. They're also much less predictable. That makes them "high risk" to my field. If high risk people are added to the pool, they increase the risk of the whole pool - there's a higher chance that average annual claims per person will be higher, and there's a larger chance that catastrophic-level claims will occur.

How does that translate into the investment analogy?

 

[Emily's Cat]

It wasn't off-topic. "American Exceptionalism," right?

There's some of that in this thread, sure... but I don't know that "How is ACA performing?" is exactly American Exceptionalism...

 

[sunmaster14]

Thanks for the run down - that is helping me see where I've gone sideways.



Okay... In the sense of just plain old variance of the distribution, yes, adding more people will make the aggregate variance lower.

But it doesn't reduce the claim level... and it doesn't reduce the risk of experiencing a catastrophic-level claim. I don't know how to make that item parallel the investment analogy.

Lets say I've got a nice happy pool of people, and I add a hemophiliac.

The likelihood that they make a claim is higher than for the other people in the pool - Their E(N) is higher. The likelihood that their claims are very expensive, given that one occurs, is also higher - Their E(S) is higher. The long left end of the tail is also fatter for a hemophiliac - that is, there's a higher likelihood of them being further out on the tail, and the chances of them having a claims that is more than 2 standard deviations away from the mean is also higher. So that would mean that this person's severity variance is higher, right?

When I talk about risk, in my bailiwick, it's generally a combination of E(N)E(S) and V(S). I *think* it's more analogous to VaR, but not so well defined.

A hemophiliac is a "high risk" policy holder. There's a much higher chance of them having very high claims than other people. They're also much less predictable. That makes them "high risk" to my field. If high risk people are added to the pool, they increase the risk of the whole pool - there's a higher chance that average annual claims per person will be higher, and there's a larger chance that catastrophic-level claims will occur.

How does that translate into the investment analogy?

The analog of expected/mean return of an investment in the insurance world would be (annual premiums - expected claims)/(required capital reserve) for a new subscriber. The analog for volatility would be the standard deviation of the distribution of claims for that subscriber. It's probably true that the claims distribution for a single subscriber is not log-normally distributed as it is for the returns on a stock, but if you add together enough well-behaved and independent probability distributions, you get a normal distribution, so I don't think that's a problem.

Frankly, I doubt that a particular individual has such high volatility in health expenses (a priori of course) that adding him to a pool would increase the volatility of the pool. The problem isn't the volatility with an unhealthy subscriber. It's the expected return. The premiums being charged are probably not sufficient to make up for the expected claims, and therefore an unhealthy subscriber has an expected negative return. An investment with a negative return is not something you want to add to your portfolio.

 

[theprestige]

LOL. Because without the americans, the world would fall to shambles, right?

It's fun to imagine what would happen if the US were no longer contributing to the check on Russian and Chinese hegemonic aims in Europe and Southeast Asia. It's also fun to imagine what would happen if the US were no longer contributing to the aid of developing nations. It is even also fun to imagine if the US were no longer contributing to the global economy. But as fun as these things are to imagine, none of them are on-topic for this thread.

 

[Emily's Cat]

The analog of expected/mean return of an investment in the insurance world would be (annual premiums - expected claims)/(required capital reserve) for a new subscriber. The analog for volatility would be the standard deviation of the distribution of claims for that subscriber. It's probably true that the claims distribution for a single subscriber is not log-normally distributed as it is for the returns on a stock, but if you add together enough well-behaved and independent probability distributions, you get a normal distribution, so I don't think that's a problem.

I almost always work with distributions built on the data, not represented by a formula. If memory serves (which it probably doesn't), we usually work with stochastic distributions not deterministic.

The severity distribution can be reasonably represented by a lognormal distribution, but it's a conditional distribution - it's the distribution of claim costs given that a claim occurred.

The frequency distribution is probably closer to an exponential... It's monotonically decreasing, and it decreases very rapidly very early, then has a realllllly long tail.

The compound distribution has *sometimes* been approximated by a punctuated lognormal - there's a substantial discontinuity at zero, for people who make no claims in the course of their policy-year.

No matter how many people we add to it, it'll never turn into a normal distribution. I don't know what it will converge to, but nothing bell-shaped, even with some skew added in.

Frankly, I doubt that a particular individual has such high volatility in health expenses (a priori of course) that adding him to a pool would increase the volatility of the pool.

I don't know what you mean by a-priori in this context.

As for impact on the pool... take a pool of people with very well understood chronic conditions or in good health. They have volatility - they could have a diabetic episode, or a severe asthma attack, or they could fall off a ladder. In which case, they're going to have claims on the order of $50K to $200K give or take (ranging from an ER visit to a couple days IP admission to stabilize). Maybe it happens, on average, about once every 3 years.

Add a hemophiliac... and it's going to shift. A hemophiliac event requiring Factor IX could happen every couple of years... and if it does happen, it will be anywhere from $500K to several million to stabilize.

The problem isn't the volatility with an unhealthy subscriber. It's the expected return. The premiums being charged are probably not sufficient to make up for the expected claims, and therefore an unhealthy subscriber has an expected negative return. An investment with a negative return is not something you want to add to your portfolio.

Yes, it is probably largely the expected return. But it's also at least partly the volatility. It's the fact that in some years those "high risk" policyholders will have low claims, and in some years they'll have 3 events instead of 0 and end up with several million in claims. It's very hard to come up with an expected claim level for them - the variance is such that it takes many, many years of data and many more people than we've got. Especially with some of the orphan conditions - there just aren't very many of them out there. Not enough to actually put together a reasonable distribution... even if we lump all the "outliers" together and look at them collectively.

We do that, by the way - we pull all of the exceptionally high cost claimants out of our pooling process, and we aggregate them separately. We look at about 5 years worth of data, and try to make a generalized "pooled high claim estimate". Even so, the accuracy of that distribution is crap.

 

[Francesca R]

I do mean independence in the sense of zero correlation.

The case of health insurance is simpler, though, because the correlations are pretty much zero.

I really don't think this is likely. Not that I have seen data. Consider somebody's cumulative health costs from when they are born to when they die. The annual increase (it never goes down) in their health charge is the return series. Or monthly whatever. Now stack a group of these return series side by side. I severely doubt that the correlation of returns is zero and suspect it is comfortably above 0.5

 

[Francesca R]

There's some of that in this thread, sure... but I don't know that "How is ACA performing?" is exactly American Exceptionalism...

Because it's exceptionally bad compared to the systems in the rest of the OECD!

 

[Emily's Cat]

I really don't think this is likely. Not that I have seen data. Consider somebody's cumulative health costs from when they are born to when they die. The annual increase (it never goes down) in their health charge is the return series. Or monthly whatever. Now stack a group of these return series side by side. I severely doubt that the correlation of returns is zero and suspect it is comfortably above 0.5

I don't follow this.

There's a very high correlation with age. As a person gets older, there costs increase - this holds true for almost everyone, but the correlation is between the costs and the individual's age. That's not the same as saying there's a correlation from one person to another.

 

[Francesca R]

I mean the return series of different individuals' health costs are pretty highly positively correlated.

They also have a systematic (negative) value.

 

[Emily's Cat]

I mean the return series of different individuals' health costs are pretty highly positively correlated.

They also have a systematic (negative) value.

I don't know what that means. I think my brain is being dumb today.

I don't know what the "return series of different individuals' health costs" means.

 

[sunmaster14]

I don't know what that means. I think my brain is being dumb today.

I don't know what the "return series of different individuals' health costs" means.

I think I understand what she's saying, but it's spurious correlation. Everybody has some predictable level of health care costs which go up each year with health care inflation. These changes in costs will have very high positive correlations between individuals because they're sort of common denominator costs for everybody, and they all go up roughly the same amount each year. But since these costs are predictable - practically fixed - they don't represent risks to the insurance company. It's the random component of health care costs that are important. I'm pretty sure that these are not correlated from person to person, unless there is some sort of cataclysmic event.

 

[Francesca R]

These changes in costs will have very high positive correlations between individuals because they're sort of common denominator costs for everybody, and they all go up roughly the same amount each year.

Quite. It makes them systematic.

But since these costs are predictable - practically fixed - they don't represent risks to the insurance company.

Of course they do. You mean that they can be quite properly priced. So can the systematic risk in financial markets.

It's the random component of health care costs that are important. I'm pretty sure that these are not correlated from person to person, unless there is some sort of cataclysmic event.

The "random" (I would say non-systematic) risks are the ones that can be diversified away by pooling them. And with typical universal insurance they are diversified away in respect of the policy holders (IE everyone) too. The systematic risk is paid for (via tax).