Independent
Thinks s/he gets paid by the post
- Joined
- Oct 28, 2006
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I'd like to pursue this a little more.
I agree that the biggest question is will the insurance company pay off. History has never shown a loss. That doesn't mean it can't happen but it's safer than a few things out there.
I don't understand the "what do people get on average" comment. If there has never been a default in history, it seems to me they get exactly what they deserve based on how long they actually live. If I die early, I understand I lost out, but at least I am dead. If I live to 100, I robbed the bank.
I thought I could put a response in a couple paragraphs. I was wrong. Sorry for the length. I probably mis-read you questions somewhere.
When I said "what people get on average" I meant the "expected value" as defined by Wiki:
In probability theory the expected value of a discrete random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff). Thus, it represents the average amount one "expects" as the outcome of the random trial when identical odds are repeated many times. Note that the value itself may not be expected in the general sense - the "expected value" itself may be unlikely or even impossible.
Note that this is exactly what Ha suggested, and the calculation method I outlined.
Here's an example. You and I agree to buy a $3,000 CD. I put in $1,000 and you put in $2,000. We let the CD interest accrue inside the CD. Say it grows to $4,000. At maturity we flip a fair coin, the winner gets the entire proceeds. The expected value of the payoff is the same for both of us - $2,000. But notice that neither one of us can actually recieve $2,000. One of use will get $0 and the other will get $4,000.
If I ask the question "What is the game worth to me?", I'll discount the final payoff to today so I can fairly compare it to my cost. The present value of the expected value of the payoff is again the same for both of us, and is $1,500 if we discount at the CD interest rate. So the game is worth $500 to me, and -$500 to you. If we played it many times, that would be our average gains and losses, even though no single round can give either of us $500.
In words that you've used, if I wanted to get the expected value of this game ($2,000 at maturity) on my own, I would need to buy a CD for $1,500 - which is $500 more than I'm putting into the game. So the game looks like a good deal to me. Similarly, it's a bad deal for you.
I don't think 86 is an unusually old age, maybe you do. Since I don't think 86 is unusual, I look at the 6% IRR. What age do you base your calculations on when you do financial planning? I think that has merit.
Again, it depends on the question. In the CD example above, the maximum payoff is $4,000 at maturity. That's an important number if you're trying to decide whether to play the game, but it's not the only number you should look at.
In an insurance policy, a couple important questions are "What's the most I could get out if this, if the really bad thing happens? And, how much will I get out of this if a kind of bad happens?" I think that's what you're doing with your live-to-86 example, calculating how the thing looks if a "kind of bad thing" (strictly in the financial sense) happens. I think that's a good question to ask and answer. But it's not the whole picture on a close decision.
I sure don't understand your "Less than they put in" (adjusted for the time value of money) comment. They pay over out time (if the insurer stays solvent) as much as CD's and bonds do. Does the "less than they put in" apply to CD's and bonds also?
On the last comment, why is a 4.5% to 7% IRR at all tied to the comment "how much do they lose on average"? Are you comparing an annuity to a 50/50 portfolio or something? I don't understand that.
Regarding bonds, let's suppose that you have a history of investing in Treasuries. But today, you're looking at a "B" rated bond. The Treasury has a 100% chance of paying each coupon and the principal on time. The B bond doesn't. It's coupon rate is higher, so if it pays off it's better than the Treasury. You can do the calculation and it might show that $900 invested in the B bond, if it pays in full, will provide as much cash as $1,000 invested in the Treasury. That's a good place to start your analysis. You now know your maximum upside. But, you also want to know the downside. Well, the issuer could go belly-up tomorrow, so the worst case is -$900. But, that's very unlikely.
Your gut tells you that there is some number between -$900 and +$100 which is some sort of average. To do that calculation, lay out a string of probabilities for the B bond paying each of it's coupons, and the maturity payment. (The probabilities are typically a decreasing string of numbers, since the issuer is probably in okay shape today, but your concern is that it will deteriorate over time.) You multiply the probabilities by the corresponding cash flows, discount to today at the Treasury rate, and that gives you a number that is somewhere between the best and worst case. If that number is less than the purchase price of the bond, then I would say you should expect to "get less than you put in (adjusted for the time value of money, which is the Treasury rate)"
In the annuity case, you do the same calculation, but the probabilities are based on a mortality table instead of the possibility of the insurer going under (because you've specified that risk is small enough to ignore). The discount rate may not be Treasuries, because you feel that you're a good enough investor to get something a little better than that. Assuming that you can get the same rate that the insurance company does, then you are using the same method that they use to price the annuity and you're using the same discount rate. If you happen to pick the same mortality table, then you will find that you're "expected loss" is exactly the present value of their expenses and profit.
So SamClem says that this method will always show a loss to you, unless you know something about your mortality that they don't (or they can get better investments than you can).
That doesn't mean you should never buy insurance. It just means that you should understand that when you add up all the policyowners of an insurance company, their total dollars back will be less than their premiums (adjusted for the interest they could have earned). You don't buy insurance because you expect to beat the insurer at it's own game. You buy because you're trying to reduce the uncertainty in your financial life, which has a value that is measured in "utility" not "dollars".