Risk Premium

[JasonScandopolous]

When one is determining rates for an insurance product, you might consider it a good idea to use your best estimate of investment yields during the time that those rates are in effect.

One way to get such an estimate is to calculate forward rates using current spot rates. However, the forward rate calculation ignores risk premium // liquidity // segmented market demand. As such, these calculations systematically overstate the actual future spot rates expected by the market.

What practical ways are there to estimate investment income? One could ignore the risk premium issue and go with the forward rates... one could use current spot rates and ignore market expectations.

Or you could come up with something that estimates risk premium for:
-various classes (gov't, corporate, etc.),
-terms (3mo, 1yr, 10yr, etc.), and
-current yield levels (i.e. risk premium estimate varies by what the current yield curve looks like; very depressed as things are now vs. 1980s, etc). And then subtract this premium from your forward rate to get a true estimated future spot rate.

Or you could select, based on judgment (or investor polls, etc.), where you think the curve will be during the period in question.

Neither of the last two seem viable. What do any of you do to address these issues?

[Eimon Gnome]

Estimating investment income is rather trivial. Buy the bonds at current market and look at the option adjusted yields. The only unknown is the default rate - so put in something for that and you are all done.

Estimating future bond prices is different. For recurring premium products, this is the trickier question. If you use anything other than the current curve, understand you are adding risk to the system. So your next question will be "what is the fair amount of compensation I should receive for taking that risk?"

[MathGeek92]

Originally Posted by JasonScandopolous

When one is determining rates for an insurance product, you might consider it a good idea to use your best estimate of investment yields during the time that those rates are in effect.

One way to get such an estimate is to calculate forward rates using current spot rates. However, the forward rate calculation ignores risk premium // liquidity // segmented market demand. As such, these calculations systematically overstate the actual future spot rates expected by the market.

What practical ways are there to estimate investment income? One could ignore the risk premium issue and go with the forward rates... one could use current spot rates and ignore market expectations.

Or you could come up with something that estimates risk premium for:
-various classes (gov't, corporate, etc.),
-terms (3mo, 1yr, 10yr, etc.), and
-current yield levels (i.e. risk premium estimate varies by what the current yield curve looks like; very depressed as things are now vs. 1980s, etc). And then subtract this premium from your forward rate to get a true estimated future spot rate.

Or you could select, based on judgment (or investor polls, etc.), where you think the curve will be during the period in question.

Neither of the last two seem viable. What do any of you do to address these issues?

Stochastically model the future environments and you will see the risk.

and what does "systematically overstate the actual future spot rates expected by the market" mean? the future spots are simple math calcs.

I can enter into a forward agreement with you and guarantee you a 10 year spot rate, 1 year from now, and pose no risk to myself. You agree to buy at the 10 year spot price. I can deliver in 1 year, a 10 year spot bond (an 11 yr spot today). You might over pay/underpay... I might sell at a loss/or a gain from where the Market price is, but I guarantee I can deliver a 10 year spot one year from based upon the forward curve.

[DixieFlyer]

Originally Posted by JasonScandopolous

When one is determining rates for an insurance product, you might consider it a good idea to use your best estimate of investment yields during the time that those rates are in effect.

One way to get such an estimate is to calculate forward rates using current spot rates.

while forward rates can be useful for hedging or for arbitrage, methinks that they have almost no predictive value for what interest rates in the future will be

[MathGeek92]

agreed... no predictive value. however, if you "need" a bond with a specified yield for the premium that you are going to recieve in the future... you can lock it in.

In a steep yield curve environment...the carry is worth a fortune, especially when you can charge customers for your ability to execute it.

[JasonScandopolous]

Originally Posted by DixieFlyer

while forward rates can be useful for hedging or for arbitrage, methinks that they have almost no predictive value for what interest rates in the future will be

Indeed... they have "some" predictive value, but they are not an unbiased estimate of future spot rates as risk and liqudity premiums are in the mix as well. This is actually why I posted in the first place; our company was operating in our assumptions as if forward rates = future spot rates.

Is there anybody here, having priced a product before with investment income expectations, that uses something better than current spot rates or forward rates to estimate the future returns on their premiums?

[JasonScandopolous]

Originally Posted by MathGeek92

I can enter into a forward agreement with you and guarantee you a 10 year spot rate, 1 year from now, and pose no risk to myself.

I'm asking what the best estimate is of future spot rates, which are the rates that a company would actually get on premiums they actually receive in a future period. Forward rates alone can't answer this question, is what I recently realized.

[JasonScandopolous]

Let me try to ask this in a different way...

When estimating investment income (or discount rates) for a product to be sold between X and Y (dates both in the future), what interest rates do you use? Current average portfolio yield? Current market yields by maturity? etc.

[MathGeek92]

Originally Posted by JasonScandopolous

Let me try to ask this in a different way...

When estimating investment income (or discount rates) for a product to be sold between X and Y (dates both in the future), what interest rates do you use? Current average portfolio yield? Current market yields by maturity? etc.

why are you trying to estimate the future sales? Are you required to issue new business? What's the purpose of the question? Are you measuring risk in providing guarantees?

[JasonScandopolous]

Originally Posted by MathGeek92

why are you trying to estimate the future sales? Are you required to issue new business? What's the purpose of the question? Are you measuring risk in providing guarantees?

Well we arent *required* to issue new business, but I sure hope that we sell some insurance! I'm trying to figure out, when we buy bonds to pay for losses on policies sold next year, what the best estimate of the yields we get on those bonds will be. I was wondering how people estimate the rates used to discount expected losses to their present value (i.e. what rates do they use in that process)?