But Why Do We Still Mix Insurance With Investments?

But Why Do We Still Mix Insurance With Investments?

In our last post Do insurance and investments mix? we explored the implications of people having a risk tolerance or risk aversion based on utility theory. We found that if people were consistent about their risk tolerance for investments and their risk aversion to large losses which they can insure against, then they should not mix their insurance and investment decisions. In short, people who can tolerate the risk of stock investments are not willing to spend much on insurance, and people who are willing to spend more on insurance usually cannot stomach the risk of investing in stocks and other risky assets. But we still see many insurance/investment products, such as investment linked insurance policies (ILPs). Why? Why do we still mix insurance with investments?

Obviously, there can be many reasons for the phenomenon we observe about human behaviour. For a start, we may still mix insurance with investments for convenience. After all, it is easier to deal with all our financial needs in one transaction than with many. But most insurance/investment products are marketed by financial advisors, so it is equally convenient to instruct the advisor to handle the insurance and investment decisions separately based on our preferences rather than having to do it ourselves.

Or, the theory could be wrong! This is not unheard of, since “all models are wrong, but some are useful“. We can try to modify the theory a bit and see where it gets us. Or, it could well be complex financial decisions such as insurance and investments can be too complex for the man in the street to fully grasp, and hence they are at the mercy of the financial professionals to make recommendations. So let’s see what else our theory can tell us about why we still mix insurance with investments.

Mixing Insurance with Investments
Do insurance & investments mix at all?

How Do We Determine Risk Aversion and Tolerance and What Does it Mean for Insurance and Investments?

Now let’s recap a bit about what we learn in the last blogpost Do insurance and investments mix?. This is also covered in a previous post Insurance: When to get insured, and when not to. Utility theory is a hypothesis that we don’t value money or wealth for itself, but for the utility or happiness it brings. In addition, the Law of Diminishing Marginal Utility tells us that the first $1,000 we gain is a big deal, and the second $1,000 is still a big deal, but less so than the first $1,000. And so on for the next $1,000, and the next $1,000 after that. So we can picture the relationship between wealth and utility as something like this

CRRA Isoelastic Utility Function for Risk Aversion = 2
Insurance and Investments - Risk Aversion 2

Due to diminishing marginal utility, our joy at getting more and more wealth does not go up in a straight line. Instead, the line is curved, and this curvature is our risk tolerance or risk aversion. What the curvature of the utility function and risk aversion tells us is how much risk we are willing to take (investment) and how much risk we do not want (insurance). For example, working through the implications of risk aversion for investments:

Real Returns Required to Invest in a Well Diversified Portfolio of Equities (Annualised volatility of 14%)
Risk Aversion LevelReal Returns Required
Risk Aversion = 1 (least risk averse)2.0%
Risk Aversion = 24.0%
Risk Aversion = 35.9%
Risk Aversion = 4 (most risk averse)7.6%

So as far as investments are concerned, the theory makes sense. The people with low risk aversion usually invest in equities. Why? Because as long as the expected return is higher than 4% in real terms (or 6% in nominal terms i.e. with inflation factored in) they can tolerate the risk. But for the people with higher risk aversion, they will only invest in bonds. Why? Again, they demand at least 5.9% in real terms (7.9%-8.9% in nominal terms) or more to invest in equities, and no honest portfolio manager is going to promise consistent returns that high!

This holds true for insurance as well:

Amount of Income/Wealth Spent to Insure against loss of 80% of Income/Wealth
Risk Aversion LevelIncome/Wealth Spent on Insurance
Risk Aversion = 1 (least risk averse)3.2%
Risk Aversion = 23.8%
Risk Aversion = 310.2%
Risk Aversion = 4 (most risk averse)23.6%

For insurance against risk of death, people with low risk aversion will not want to spend more than 3% to 4% of their income/wealth on insuring themselves. A check on the insurance premium comparison site CompareFIRST.sg show that for someone aged 34 looking to insure himself for 30 years, the annual premiums come out to about $700 for coverage of $1 million. Or, over 30 years, total premiums amount to 2.1% of the sum assured, which is within the limits of how much they are willing to spend.

For the people who are more risk averse, they will be willing to pay more for insurance, either insuring themselves for a longer period (say 40 years), or for a larger amount, or by adding on riders such as coverage for critical illness. Again, a check on CompareFIRST.sg shows that the same person aged 34 will pay about $3,500 annual for 40 years of term life insurance plus critical illness coverage. Or, total premiums of about 14% over 40 years of the sum assured. Which is again within the bounds of what the theory indicates they are willing to pay.

So far, nothing indicates that we are on the wrong track, as the implications of using risk aversion to gauge appetite for insurance and investments seem reasonable. What it implies is that there are two groups of people, the first group who spend less on insurance and are willing to invest in stocks, and a second group which spends much more on insurance and confine themselves to low risk investments, like bonds and deposits.

Two Groups of People with Different Risk Tolerances Making Decisions on Insurance and Investments
Why do we mix insurance with Investments?
  1. The first group of people, with low risk aversion/high risk tolerance, will never mix insurance and investments. They will also invest in risky assets like stocks for higher returns.
  2. The second group of people with higher risk aversion/lower risk tolerance will gladly pay higher premiums for insurance, but will largely confine themselves to deposits and bonds, for low risk and low returns. Some of these people will mix insurance and investments, but the investments are largely of the low risk kind. For example, short term insurance bundled with deposit-like returns have been popular in the past with these people (such as the Singlife Accounts)

What Could Be Wrong With The Way We Determine Risk Aversion and Tolerance?

But there is also a third group of people in addition to the two groups above, and who mix insurance and investments, not just the low risk low returns sort, but in stocks. These are purchases of Investment Linked Insurance Policies (ILPs), which are sometimes linked to stock investments that can account for this behaviour, which does not seem plausible in the expected utility framework?

The easy answer would be to say that the expected utility framework is wrong, or not useful, but as we see above, there are some predictions the framework makes on the returns expected on stock investments, and the amounts we spend on insurance which seem to be reasonable and in-line with real world observations. Perhaps some modifications in the framework might give us different results?

One modification which we can explore is the curvature of the utility function, which determines our risk aversion or risk tolerance. Now, for every person who retired with millions in the bank who says that they wished they had not worked so hard for the last extra million dollars (i.e. the diminishing marginal utility of wealth), there is another with millions in the bank and yet who is considering working one more year before retiring (i.e. marginal utility of wealth does not diminish). What this means is that the utility curve may not curve as sharply as our wealth increases. This would mean it looks something like this:

Utility Function assuming no Diminishing Marginal utility of Wealth from current level
Why do we still mix insurance with investments?

As mentioned earlier, it is easy to find examples of people with enough money in the bank, but are just as passionate about pursuing the next million dollars. Expected utility which is based on each increment of wealth being worth less to us than the previous one works well with the benefit of hindsight, but decisions about investments are usually made without the benefit of this, so this could be a viable model of how we make decisions, even if it is not how we feel about it on reflection later!

What would such a utility function imply for investments? As far as insurance is concerned, there is no difference, since the curvature of the utility function as we get lower and nearer to zero wealth is unchanged from the previous examples in our post Do insurance and investments mix?. But for investments, the unchanging desire for higher and higher returns makes quite a bit of difference!

Real Returns Required to Invest in a Well Diversified Portfolio of Equities (Annualised volatility of 14%)
Risk Aversion LevelReal Returns Required 
Risk Aversion = 1 (least risk averse)1.02%
Risk Aversion = 22.04%
Risk Aversion = 33.04%
Risk Aversion = 4 (most risk averse)4.07%

Unlike previously, when the most risk averse require a real return of at least 7.6% to invest in stocks, here, they might do so if the investment manager promises a real return as low as 4%!

Hence, interestingly, if we hanker after the next million dollars and the next million after that (what do we call this, greed?), we see that even the most risk averse among us will be willing to invest in risky assets like stocks, derivatives and even cryptocurrencies! And these will be those in the third group who will continue to mix insurance with investments.

What Does All This Tell Us About Mixing Insurance and Investments?

Strictly speaking, if we could assess everybody’s risk tolerance or risk aversion accurately, and made recommendations based on it, there would be no instance where people will mix insurance with investments in risky assets. But this mixing of insurance and investments occurs everyday in the real world.

This potentially points to two conclusions:

  • People make decisions about investments looking to the upside, and without the benefit of hindsight. Therefore, they may end up being very disappointed when things do not pan out
  • The whole process of assessing risk tolerance and risk aversion (a standard requirement for financial advisors) is actually quite useless, due to 1. above, which means people will say something that justifies their investments

In the meantime, we will continue doing inaccurate risk tolerance assessments, not heeding what they tell us, and mixing insurance and investments!

Do Insurance and Investments Mix?

You can read some of our other blogposts on insurance here:



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