Life and Death

Do you know what you’re buying when you take out a term life insurance policy?  You may have a sense that you’ve gained some protection against catastrophe.  But what specific benefit did you buy and was it worth the cost?  I’m going to show you that you’re buying this shape, what it is, and why it’s important:

Assumptions

A hypothetical husband and wife, age 30, are deciding if they need life insurance policies using the following metric:

  • Success = Husband and wife die and no one ran out of money.
  • Failure = Husband and wife die, but someone ran out of money.

Income and Savings

  • They each take home $50,000 per year until retirement at Age 65.
  • They live on $70,000 per year, saving the rest towards retirement.

I’ve used my regular model to project the future, but I added a wrinkle: Using the actuarial tables from the social security administration I gave each person a corresponding chance to die each month!

Death and Insurance

  • If one partner dies, the other continues to make $50,000 per year until retirement but has $50,000 in expenses every year they are alive.
  • If the couples decides to get 30-year term life insurance, the women pay $1200 per year for $500,000 coverage.  The men pay $1400 per year for the same coverage(Note: Your insurance premium rate may be different, the above numbers are close to the average the insurance industry needs to charge to make a profitable transaction.  I’m not breaking this out into smoker/non-smoker, etc, but you should stop smoking!)  
  • If they don’t get life insurance, they have extra money to put each month towards becoming self-insured.

Everyone Dies

I randomly paired off 1,000 couples and predicted their deaths from the above actuarial data (I highlighted a few couples on the graph, to help you interpret the data points properly):

Figure 1: A Thousand Couples: Age of death for husband (x-axis) and wife (y-axis)

This has some obvious limitations – people get remarried, a partner’s death may or may not be correlated with your own.  But let’s proceed under the assumptions above and find out if life insurance adds value for the cost.  I analyzed each couple’s retirement outcomes using the above assumption with a 30 year level term life insurance policy in place, and again without any life insurance.

Results – No Life Insurance

With no life insurance, our thousand couples put 30% of their working income towards their nest eggs each month.  93% of the couples die with a positive net worth (Success!), while 7% die with a negative net worth (Failure).  Here’s a sample of couples where eight succeeded in maintaining positive wealth until death, and two failed to do so:

Eight Couples Succeed, Two Fail
Figure 2: A sample of ten couples and their retirement account value paths

The graph above gets pretty messy pretty quickly, but you can see which couples outlived their money and which did not.  Let’s revisit Figure 1 and note the couples who succeeded and those who failed:

Which couples succeeded and failed with no life insurance
Figure 3: Each couple’s financial net worth at death: Success or Failure

It’s hard to pick out a clear pattern in the data above, but notice a collection of red failure dots grouped in the region where the husbands died young and the wives outlived them for many years. The current assumptions of the model also predict hardship for a small share of couples in their 80s and 90s, suggesting they did not save enough during their earning years and that they should curtail their spending in retirement.

As a group, there’s a wide range of financial trajectories:

Figure 4: 10% Best, 10% Worst, and Expected Case for Retirement with No Insurance

The disparity in net worth shown in Figure 4 is somewhat surprising given that each couple starts at the same age, with the same (zero) funds, the same income, and the same saving/spending plan.  The only variables are the uncertainty of market returns and the uncertainty of death.  Some of the couples see their retirement assets take off, exceeding $10 million.  However, 7% of the couples die with a negative account – these are the failures we should worry about.

Will life insurance help the “Many Failures” region above, or will it further diminish the resources of couples that live into their eighties and beyond?

Results – With Life Insurance

We’ll hold everything exactly the same and run the analysis again, but we’ll include a 30 year term life insurance policy that costs each woman $1200 per year and each man $1400 per year.  Each person that dies before they turn 61 receives a credit of $500,000 directly added to their retirement account value.

Figure 5: Who gets paid by their life insurance policy

So what impact does life insurance have on our pool of couples?  It reduces the number of failures when someone dies during the term they are insured, but it also reduces the level of wealth for surviving couples, especially those who live into their eighties and nineties.  Overall, the failure rate is reduced from 7% to 5%.

Figure 6: Results of the simulation for all couples with life insurance

The insured couples essentially never ran out of money before Age 80, in contrast to their uninsured counterparts who were more likely to be imperiled by lost income from a death at a young age.  However, a few more couples in their elderly years fell into the negative zone due in part due to the drain of insurance premiums during their working years.  They invested less and outlived their nest eggs.

Figure 7: Projections of the best and worst case scenarios when life insurance is included

Take close note of the Figure 7 compared to its uninsured counterpart.  The worst case scenario is not quite as bad.  However, the best case scenario is somewhat diminished.  Though it might be hard to notice the difference between $10.7 million and $10.2 million in the best case, you’re certain to feel the difference between $0.7 million and $0.2 million in the worst case.  Insurance reduces the volatility of your long term savings.

Conclusions

  • Life insurance will help secure the surviving spouse’s future from the catastrophe of an unexpected death at a young age.
  • Life insurance increased the likelihood of dying with positive net worth, but reduces the potential investment returns over the long run.
  • You should buy life insurance, but only as much as you need: It is insurance and not an efficient investment.

The benefit of life insurance is that it removes a particular slice of downside scenarios.  The highlighted blue shape at the top of this article is reproduced in the following graph.  It is exactly what you’re buying when you buy life insurance: Protection from the worst case scenarios of your financial life.

A graph showing the difference in worst case scenarios with and without life insurance.
Figure 8: The benefit of life insurance against downside loss

The cost of life insurance is that, on average, you won’t get out of it what you put into it.  Buying life insurance means you have less money to protect against other risks, and you have less upside potential in your long term investments:

A graph showing the loss in upside potential due to the cost of life insurance premiums.
Figure 9: The cost of life insurance on upside potential

The reason life insurance exists is because it has value.  You may give up some potential in the best case scenario, but if a series of unfortunate events should befall you, the benefits of being properly insured cannot be overstated.

Addendum

I also want to note that the above situation is for a family with two matching incomes.  In a single income family, or one with a high earner, it is (usually) imperative that insurance be purchased for the high/solo earner.  You should buy insurance for unlikely events that would ruin you or those who depend on you.  Refrain from buying insurance for events that won’t alter your life.

If your savings rate is very low, you may need to sacrifice the comfort of a good insurance policy for the more pressing issue of saving to meet your needs if you do survive to an old age.  The same simulation looks very different for a couple with a lower savings rate because the insurance premiums take away a larger chunk of their investment funds.  (Learn more about the importance of savings rates in Case 3: The Four Physicians.)

Your situation is unique.  Use the framework above to think about the cost and benefit of insurance in your life.  If you find you are under insured, do something about it.

 

 

 

 

4 Replies to “Life and Death”

  1. Awesome analysis! I love the 4 quadrant chart to show all four scenarios. Life insurance company shoiluld hire you.

    A couple people have covered it on other blogs but I am going to put a post together talking about the tiered structure rather than buying one plan which can help on the cost side.

    1. Thanks! Yeah I have plans to get into more details about what and how to buy life insurance, once you’ve made the decision to do so. The goal of this post was just to show what exactly you’re getting protection from. It was super fun to crunch the numbers with a variable I labeled “DEATH FACTOR”.
      My own term life insurance slowly becomes less valuable over time as I didn’t get a COLA rider. I figured as the years go by I’ll need less and less insurance so I’m letting inflation slowly chip away at my coverage… If I have another kid though, I’ll be all over that tiered structure. Cheers, Mouse

  2. Wow. Honestly I love this type of deep analytical stuff (stuff unfortunately that I’m not good at myself). Great way to break down pros/cons of life insurance. I just subscribed to your blog and look forward to more innovative ways to approach things.

    1. Thanks xrayvsn, comments like yours really make the time and effort going into this analysis worth it for me. And I 100% appreciate the subscription, I’ll try to make it worth your while!

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