The risks you can’t diversify away

Everything else in this series has been about risks you can shape: size a position, spread it across things that don’t move together, avoid leverage, keep your broker honest. Some risks don’t bend to any of that. If a household’s main earner dies, the income stops — all of it, at once — and no asset allocation fixes that.

There are four things you can do with a risk: avoid it, reduce it, retain it (carry it yourself), or transfer it to someone else for a price. Insurance is the last one. You pay a small, certain amount — the premium — so that a large, uncertain loss lands on an insurer instead of on you. The insurer can carry it because it pools thousands of similar risks, most of which never claim.

Term life insurance is the plainest form: you pay premiums for a fixed term; if you die during it, the insurer pays the sum assured; if you don’t, it pays nothing. No maturity value, no return. That’s not a flaw. It’s what makes it pure risk transfer.

This post is about mechanics. It doesn’t recommend any product, insurer or amount of cover, and every number in it is a clearly labelled illustration.

The formula

Expected claim cost for one year  =  probability of death × sum assured
Premium  ≈  expected claim cost  +  the insurer's expenses, capital cost and margin

Needs-based cover (one common way to size it):
    Cover  =  PV (present value) of the household's future expenses
            +  outstanding loans
            +  future goals (education, a wedding)
            −  existing investments that could meet them

PV of a fixed yearly amount E for n years at rate r:
    PV  =  E × [1 − (1 + r)^(−n)] / r

The savings return inside a bundled (insurance + savings) plan:
    the IRR (internal rate of return) that makes the premiums you pay grow into the maturity value

The needs-based formula is discounting turned around: instead of asking what future cash flows are worth today, it asks what lump sum today would replace them. Using a real rate (after inflation) keeps the expenses in today’s rupees; the real returns post shows why the difference matters.

🧒 Explain it like I'm 10 (optional — skip if this is already clear)

A thousand kids each put ₹20 in a jar at the start of the year. If any kid’s bicycle gets stolen, the jar buys them a new one.

Most years, only a few bikes get stolen, so most kids “lose” their ₹20 — but nobody has to face buying a whole new bicycle alone. You’re not paying ₹20 to make money. You’re paying ₹20 so that one bad day doesn’t wreck your year.

Now imagine a jar that promised to give everyone back more than their ₹20 at the end, and buy stolen bikes. It would have to charge a lot more than ₹20. That’s the difference between plain insurance and a plan that bundles savings in.

Worked example: a hypothetical household

Everything here is invented to show the method. Real needs depend on the household, and a real premium depends on age, health, term and the insurer.

Step 1: how much cover?

Component Assumption (hypothetical) Amount (₹)
Household expenses to replace ₹6,00,000 a year for 25 years, at a 2% real rate 1,17,14,074
Outstanding loans Home loan balance 30,00,000
Future goals Children’s education, in today’s rupees 20,00,000
Less: existing investments Savings that could be used −15,00,000
Cover needed   1,52,14,074

Rounded up to the next ₹25 lakh: ₹1.75 crore. Note what drives it. The expenses line — 25 years of a family’s life — is most of the total: about 19.5 times a year’s expenses on its own. That’s why a round number that merely “sounds like a lot” can fall far short.

Step 2: what is the insurer actually charging for? Suppose, purely for illustration, a one-year chance of death of 1 in 1,000 (not an estimate for any real person or age). The expected claim cost on ₹1.75 crore of cover that year is ₹17,500. The premium is that plus the insurer’s costs and margin — so on average the policyholder pays more than they expect to get back. That’s true of every insurance policy and it’s fine: you aren’t buying an expected profit, you’re buying the removal of a loss that would be ruinous. The Kelly post made the same point about betting: some outcomes are worth paying to avoid because you can’t recover from them.

Step 3: the savings inside a bundled plan. Many policies combine insurance with savings: you pay more, and get a maturity value back. Take a hypothetical plan: ₹1,00,000 a year for 20 years (paid at the start of each year, ₹20,00,000 in total) and a maturity value of ₹30,00,000 at the end.

Hypothetical bundled plan  
Total premiums paid (₹) 20,00,000
Maturity value (₹) 30,00,000
IRR of premiums into maturity value 3.72%
The same premiums compounded at 6% a year (₹) 38,99,273
The same premiums compounded at 8% a year (₹) 49,42,292

The 3.72% is the return on the savings part including the cost of the life cover it carries, so it isn’t a like-for-like comparison with a deposit or a fund; the compounding rows are arithmetic at round rates, not forecasts. The point is the method. Any bundled plan’s guaranteed maturity value can be turned into an IRR (the XIRR post shows how), and then you can see what you’re earning on the savings and ask whether you’d buy the cover and the savings separately. How premiums and payouts are taxed changes the answer and is covered in the tax series.

Why this closes the module

Read back through this series and one idea keeps returning: stay in the game. The arithmetic of losses showed that deep losses need huge gains to repair. Position sizing, Kelly and leverage were all about never taking a bet that can end you. Concentration, liquidity, currency, inflation and counterparty risk, and outright manipulation, were about losses that arrive from directions the price chart doesn’t show. Insurance is the same idea applied to your life instead of your portfolio: identify the loss you couldn’t recover from, and don’t carry it alone.

Common mistakes

  • Judging insurance by whether you “got your money back”. A term policy that never pays out did its job: it carried the risk for the whole term. Wanting a return from insurance is how people end up paying for bundled savings they’d never choose on their own.
  • Picking cover by a round number. Cover sized by what “sounds like a lot”, rather than by what it must replace, is, in our view, one of the commonest ways to be under-insured. Do the needs arithmetic, even roughly.
  • Insuring the wrong person. Life cover replaces income. Cover on a child, with no one depending on their earnings, transfers very little risk.
  • Letting the cover end before the need does. Term cover transfers risk only for its term. If the loans run for 20 more years and the children depend on the income for 25, a shorter policy leaves the last years uncovered.

Sources

Takeaway: Insurance is for losses you can’t afford to carry, not for returns — you pay a small certain cost so that a large uncertain one lands on someone else. Size life cover by what it must replace, and if a policy bundles in savings, turn its maturity value into an IRR before you judge it.