Re: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
Dave Ingram
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.There are a number of ways of getting at the’ risk adjusted’ value of a set of risky cash flows. Two of them are:· Discount the expected cash flows at a risk adjusted discount rate; or· Discount the risk adjusted cash flows at the risk free rate.Generally in financial economics you do the latter – apply a change of measure / change probabilities to risk adjust the cash flows then discount at the risk free rate (then take an average). The CoC risk adjusts the cash flows more directly – by adding an explicit risk charge. The discount rate should still be the risk free rate, though.Some other observations:· This doesn’t really ‘solve the problem’ though. It changes the question from ‘what is the appropriate discount rate?’ to ‘what is the correct amount of capital to hold?’;· This method is not the preferred method in Australia (at this moment in time). For many years we have used a quantile approach to setting regulatory risk margins (this is a valid approach – just different. This may change over time, as it is not usually wise to be arbitrarily different;· Another approach (more theoretically correct, I suspect, or at least esily reconciled to traditional change of measure pricing) would be to apply a transform (E.g. Esscher Transform) to the distribution of cash flows. In this case the unknown is a risk aversion parameter.In the absence of a price for similar sets of cash flows you can’t interpolate to price your own cash flows. Any convention that is easy to implement will do.Steve.From: Zimmerman, Darin [mailto:Darin.Z...@transamerica.com]
Sent: Thursday, 24 June 2010 3:03 AM
To: in...@list.soa.org
Subject: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital methodThe short answer is that I think your proposal amounts to “double counting”.The long answer starts with the reminder that the “CoC method” is a theoretical approach (market consistent) to explain a market-observed priced.Let’s suppose a highly rated bond is trading at a 25 bps premium. This is the old way of pricing risk. We take the expected profits (the coupons) without margins and discount them at a risk adjusted rate (risk-free plus 25 bps). This “explains” the market observed price.Also in the real world, If I hold this bond, I also need to hold capital to protect against loss of the bond. Typically, a highly rated bond might only require 4.166667% additional capital (6% of 4.16667% equals 25 bps). Discounting the explicit margins at the risk free rate also explains the current market observed price.If we were to discount explicit margins at a risk-adjusted return, we wouldn’t bear resemblance to the actual capital we hold in the real world.CheersFrom: Hans Waszink [mailto:in...@waszinkadvice.com]
Sent: Wednesday, June 23, 2010 12:19 PM
To: in...@list.soa.org
Subject: INARM Message - Risk Margin and the Cost of Capital methodAll,I would like to use this forum to discussing the following issue.The 'Cost of Capital' methodology for determining risk margins of insurance risks now seems to have become the preferred methodology worldwide, see for example:The method is simple and elegant, and has a lot of intuitive appeal. The approach is briefly as follows:* In the absence of a liquid market for insurance risks, the margin is determined as the cost of capital for the entity assuming the risk .* The cost of capital is then determined as the present value of all future required returns to the provider of the capital. The periodic return to the capital provider is the reward that (s)he requires commensurate with the risk inherent in the assumed liability. Typically the required return is set at 6% in excess of the risk free rate annually.* The risk margin is then determined as the the present value of all these future 6% returns, discounted at the risk free rate yield curve.It is in this last point where I see a problem. It seems that by discounting the future return to the capital provider at the risk free rate, one assumes that these returns are valued as if they were risk-free. But it is precisely because they are not risk free that the capital provider recieves them. So to be consistent, the discount rate should be the required rate of return and not the risk free rate.Say for example, the required capital is 100, and the required return 6%. Thus the annual expected return to the capital provider is 6 (in excess of the risk free rate).Suppose the capital needs to be held for 50 years. Assuming the best estimate scenario will unfold, the full capital of 100 will then be returned to the capital provider. In a worst case scenario, none of the capital may be returned, and for this risk the capital provider needs to be rewarded extra .By discounting the annual cashflow of 6 at the risk -free rate, one is assuming that the capital provider would be indifferent between recieving the annual release of the risk margin of 6 on average or, for example, a fixed coupon of 6 from a 50 year German government bond .Also, discounting the annual return of 6 at the risk free rate of say, 2% on average, over a long period, will lead to the cost of capital being higher than the capital itself. Discounting an annual casfhlow of 6 at a discount rate of 2% over 50 years yields a present value of 188. Thus the cost of capital is higher than the capital itself.Both these results seem completely anomalous to me. Surely any sound investor would prefer a risk free return on a government bond over a risky pay-off from an insurance enterprise in the same (expected) amount. Moreover, if the risk margin exceeds the required capital itself, then one could make an instantenous profit by assuming the liability, recieving the risk margin, putting up the required capital and taking the rest as gain. This would be an arbitrage opportunity, which is exactly what one tries to avoid by estimating market value.I am curious to hear whether anyone has come across this issue, or has any opinion on the matter.Kind regards,Hans Waszink MSc MBA AAG
Waszink Actuarial Advisory
IJsvogellaan 17
2261 DL Leidschendam
The Netherlands
phone# +31-(0)70-3203115
www.waszinkadvice.com
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From: Dave Ingram [mailto:davei...@optonline.net]
Sent: Thursday, 24 June 2010 9:46 AM
To: Stephen Britt
Cc: Zimmerman, Darin; in...@list.soa.org
Subject: Re: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
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From: Stephen Britt [mailto:Stephe...@iag.com.au]
Sent: Thursday, 24 June 2010 10:03 AM
To: Dave Ingram
Cc: Zimmerman, Darin; in...@list.soa.org
Subject: [Spam] RE: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.
On the first question, the CoC approach is able to exactly match the price of two similar securities, simultaneously. There are two variables in the CoC approach – the risk charge and the amount of capital you need to hold against the security. You should be able to set parameters for these two which recovers the ‘price’ of the two instruments. Whether these prices are reasonable when assessed as a whole, I don’t know.
I’ve never thought about using the CoC approach to value an asset on the books of an entity, just the untraded liabilities. Is the CoC considered a viable approach to valuing assets?? (Yes one man’s asset is another man’s liability…)
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From: Dave
Ingram [mailto:davei...@optonline.net]
Sent: Thursday, 24 June 2010
9:46 AM
To: Stephen Britt
Cc: Zimmerman, Darin;
in...@list.soa.org
Ingram, Dave
The "valuation" model that is usually used for traded assets where there might not be a price right when you want it is to take a valuation model like the Black Scholes model and "back into" a parameter, usually volatility so that the model reproduces the price of a similar security. Then that implied volatility parameter is used to value the temporarily untraded security.
What I am suggesting is an equivalent process where one would "back into" a COC rate for a traded security. Given the expected cashflow and the Solvency 2 specified Economic Capital, find the COC that then added to the PV of cashflows reproduces the price.
Do this for a basket of securities and find out of any two similar securities result in a similar COC.
Do it over time for the same securities and see if the COC is at all stable.
This has always seemed to me as the most simple minded proof of concept.
Dave
David Ingram, CERA, FRM, PRM
Willis Re
+1 212 915 8039
From: Stephen Britt <Stephe...@iag.com.au>
To: Dave Ingram <davei...@optonline.net>
Cc: Zimmerman, Darin <Darin.Z...@transamerica.com>; in...@list.soa.org <in...@list.soa.org>
Sent: Wed Jun 23 19:03:17 2010
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Frank Ashe
From: McCoy, Jacob [mailto:McCoy...@principal.com]
Sent: Thursday, 24 June 2010 10:01 PM
To: in...@list.soa.org
Subject: RE: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
So everyone likes the CoC method. It's a simple formula which you can calculate in an excel spreadsheet. I like that, but it ignores today's modern computing power.
Why is it that people ignore quantile methods (CTE, percentile) approach to solving for risk margin? The cost of capital method has two subjective measures (rate of return and capital amount). It seems like those flaws are being over looked because it is computationally easy.
One final point, the CoC method is considered intuitive because it is similar to traditional actuarial methods.
From: Kelliher,
Patrick [mailto:Patrick....@scottishwidows.co.uk]
Sent: Thursday, June 24, 2010 5:04
AM
To: Dave Ingram; Stephen
Britt
Cc: Zimmerman, Darin;
in...@list.soa.org
Subject: RE: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
Simple example which may help ?
Suppose in one years time I have a management charge due of 1% of an equity fund presently worth £1m.
Assuming a 5% risk-free rate and a 3% equity risk premium, my "real world" expected cashflow is £1m x 1% x (1 + 5% risk-free + 3% premium) = £10,800.
However unless this is hedged, I need to hold Economic Capital (EC) against a shortfall in the cashflow due to falling markets. Assume we need to set aside £5,000 now to cover a fall in equities in one years time at a certain confidence level (ca.50%) - at that time, the cost of that capital is 6% x £5,000 = £300.
The expected cashflow less the cost of capital gives £10,500 in one years time, and discounting this at the risk-free rate would give a present value of £10,000.
The risk-neutral and (one would hope) market consistent approach would be to roll up the fund at the risk-free rate, giving a cashflow of £10,500 in one-years time and a present value of this of £10,000.
Its a bit crude but I hope it illustrates that the two approaches should give the same result. I would also note that 6% is not set in stone but should be a function of the confidence level you choose for EC and by implication an organisation's target rating. The higher the rating, targeted the greater the EC buffer required but a higher rated entity should be able to raise capital more cheaply so its cost of capital should be lower. I also see a link between EC, the cost-of-capital and the equity risk premium you assume.
From: Dave
Ingram [mailto:davei...@optonline.net]
Sent: 24 June 2010 00:46
To: Stephen Britt
Cc: Zimmerman, Darin; in...@list.soa.org
Subject: Re: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
The way that I like to think of it is that all risk should be included once and only once in the calculation. So either in the discount rate or in the cashflows. But not both.
I have had two questions about the cost of capital method:
1. Has anyone checked if it is even remotely close to what you get for a market traded risk? What I mean is if you deconstruct a market traded risk and solved for the market consistent COC that reproduces the price are there any examples that give an even slightly similar result?
2. This method makes the untraded risks on the balance sheet seem like the most stable things while the traded risks will bounce around as market based risk margins bounce up and down. I think that it send an exact backwards message about the desirability of traded vs. untraded risks.
So my suggestion would be to combine the two ideas and create an index of market implied COC that would be used to adjust the 6% standard COC up and down as the market gets more and less risk adverse. Otherwise the system seems to incent shifting into untraded risks whenever the market risk margins go up.
Dave Ingram
On Jun 23, 2010, at 6:01 PM, Stephen Britt wrote:
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.
There are a number of ways of getting at the' risk adjusted' value of a set of risky cash flows. Two of them are:
· Discount the expected cash flows at a risk adjusted discount rate; or
· Discount the risk adjusted cash flows at the risk free rate.
Generally in financial economics you do the latter - apply a change of measure / change probabilities to risk adjust the cash flows then discount at the risk free rate (then take an average). The CoC risk adjusts the cash flows more directly - by adding an explicit risk charge. The discount rate should still be the risk free rate, though.
Some other observations:
· This doesn't really 'solve the problem' though. It changes the question from 'what is the appropriate discount rate?' to 'what is the correct amount of capital to hold?';
· This method is not the preferred method in Australia (at this moment in time). For many years we have used a quantile approach to setting regulatory risk margins (this is a valid approach - just different. This may change over time, as it is not usually wise to be arbitrarily different;
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Stephen Britt
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.
There are a number of ways of getting at the’ risk adjusted’ value of a set of risky cash flows. Two of them are:
· Discount the expected cash flows at a risk adjusted discount rate; or
· Discount the risk adjusted cash flows at the risk free rate.
Generally in financial economics you do the latter – apply a change of measure / change probabilities to risk adjust the cash flows then discount at the risk free rate (then take an average). The CoC risk adjusts the cash flows more directly – by adding an explicit risk charge. The discount rate should still be the risk free rate, though.
Some other observations:
· This doesn’t really ‘solve the problem’ though. It changes the question from ‘what is the appropriate discount rate?’ to ‘what is the correct amount of capital to hold?’;
· This method is not the preferred method in Australia (at this moment in time). For many years we have used a quantile approach to setting regulatory risk margins (this is a valid approach – just different. This may change over time, as it is not usually wise to be arbitrarily different;
Stephen Britt
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.
On the first question, the CoC approach is able to exactly match the price of two similar securities, simultaneously. There are two variables in the CoC approach – the risk charge and the amount of capital you need to hold against the security. You should be able to set parameters for these two which recovers the ‘price’ of the two instruments. Whether these prices are reasonable when assessed as a whole, I don’t know.
I’ve never thought about using the CoC approach to value an asset on the books of an entity, just the untraded liabilities. Is the CoC considered a viable approach to valuing assets?? (Yes one man’s asset is another man’s liability…)
–––––––––––––––––––––––––––––––––––––––––––––
STEPHEN BRITT
SENIOR MANAGER
INTERNAL CAPITAL MODELS
INSURANCE AUSTRALIA GROUP (IAG)
T +61 (0)2 9292
2311
F +61 (0)2 9292 3159
M +61 (0)411 014 571
E stephe...@iag.com.au
www.iag.com.au
PLEASE CONSIDER THE ENVIRONMENT
BEFORE PRINTING THIS EMAIL.
–––––––––––––––––––––––––––––––––––––––––––––
From: Dave Ingram
[mailto:davei...@optonline.net]
Sent: Thursday, 24 June 2010 9:46 AM
To: Stephen Britt
Cc: Zimmerman, Darin; in...@list.soa.org
Frank Ashe
To: in...@list.soa.org
Subject: [Spam] Re: [Spam] RE: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
----- Original Message -----From: Stephen BrittSent: Monday, June 28, 2010 3:26 AMSubject: [Spam] RE: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.
BTW Hank, I don't agree with your requirement 2. There is no forced inequality between quantum of risk margin and capital required. The quantum of risk margin is a one-off addition to a transaction which must support capital for the length of the investment. The risk margin is the present value of a series of cash flows. When money is cheap the risk margin will need to be higher.
Don't confuse capital with claims paying capacity. Claims paying capacity is the sum of:
1. Present value of expected claims; plus
2. Risk margin; plus
3. Capital.
I see no reason for 3 to be greater than 2. They are linked, in that they should both increase with the riskiness of 1.
Steve.
---------------------------------------------
STEPHEN BRITT
SENIOR MANAGER
INTERNAL CAPITAL MODELS
INSURANCE AUSTRALIA GROUP (IAG)
T +61 (0)2 9292 2311
F +61 (0)2 9292 3159
M +61 (0)411 014 571
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BEFORE PRINTING THIS EMAIL.
---------------------------------------------
From: Hans Waszink [mailto:in...@waszinkadvice.com]
Sent: Sunday, 27 June 2010 7:20 PM
To: in...@list.soa.org
Subject: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
Some further thoughts on this issue. The following seems to reflect the commonly held view:
There are a number of ways of getting at the' risk adjusted' value of a set of risky cash flows. Two of them are:
I Discount the expected cash flows at a risk adjusted discount rate; or
II Discount the risk adjusted cash flows at the risk free rate.
It should be possible to formulate requirements that the methodology for a risk margin should adhere to. The ones I can think of right now are:
1. For a liability, the margin should increase with the risk taken;
2. When using the cost of capital method, the risk margin should be no greater than the highest amount of capital required at any one point in the projection (Cost of Capital <= Capital).
I'm sure these are not the only ones though.
Anyway I conclude that neither method I nor II above satisfy both requirements 1 and 2 . Increasing the discount rate to reflect higher risk decreases the present value of the cashflows, hence the value of the liability will be lower. This is a well know conundrum in corporate finance theory. When you value the profit streams of a venture, the higher the discount rate, the lower the PV of the profit. But when all the profit streams are negative, then higher risk implies a higher/ less negative PV.
Method II on the other hand when used as part of the CoC method satisfies 1 but not 2. Simply take an annual cashflow of 6% and discount at 2%. When the time horizon is long enough, the PV will exceed 100%, and converge to 300%.
Also the two methods cannot be equivalent. When risk adjusting the cash flows of a liability, you add the risk margin. This increases the present value. Then shifting from the risk adjusted discount rate to the risk free rate, you also increase the PV. So the second approach is always higher then the first
I think the core issue is with the assumption of equivalence between the the risky cashflow plus margin, and the risk free cashflow, in combination with the CoC method.
At a fixed point in time, you may say the holder of a liability is indifferent to either having to pay an uncertain cashflow of x, or a certain cashflow of x + margin, with some method to determine the margin (parameter and method also under debate). We then take the latter and treat it as it if were a risk free cashflow.
However, when you bring in discounting, the two propositions (uncertain CF of x or a certain CF or x + margin) are far from equivalent from the capital provider/investor's point of view.
When faced with the certain CF, the PV is simply the CF stream discounted at the risk free rate. There is no capital to hold, no risk and no profit to be made.
But in the second case of the uncertain CF, there is an initial capital investment, an annual return and hopefully a return of the investment at the end date.
Now what is the appropriate discount rate for this stream of expected cashflow to the investor? From the investor's point of view, the net cashflow is not the liability cashflow, but the release of the risk margin after the liability payment to the policyholder.Now we are back to the old question of how to value a risky investment.
There is an expected annual cashflow, the present value of which must reflect the risk inherent in the cashflows. The proposition to the investor is: invest capital in the beginning, and recieve the annual release of risk margin as cash flow. We can use method I or II above to do the valuation. Method I is the 'old world' methodology of discounting at the risk bearing rate. In this case, the canonical discount rate would be the required return that was used to set the risk margin in the first place.
When applying method II, you can use the risk free rate, but it would require a downward adjustment of the risky profit stream to the investor. Hence although the required return on capital may be 6%, to determine the present value of the stream of 6% annually using the risk free rate, you would have to make a downward adjustment to the 6% to reflect the riskiness of this cashflow to the investor.
How to make this adjustment?
Maybe the CoC approach is not so simple and intuitive after all...
Hans
----- Original Message -----
From: McCoy, Jacob
Sent: Thursday, June 24, 2010 2:01 PM
Subject: RE: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
So everyone likes the CoC method. It's a simple formula which you can calculate in an excel spreadsheet. I like that, but it ignores today's modern computing power.
Why is it that people ignore quantile methods (CTE, percentile) approach to solving for risk margin? The cost of capital method has two subjective measures (rate of return and capital amount). It seems like those flaws are being over looked because it is computationally easy.
One final point, the CoC method is considered intuitive because it is similar to traditional actuarial methods.
From: Kelliher, Patrick [mailto:Patrick....@scottishwidows.co.uk]
Sent: Thursday, June 24, 2010 5:04 AM
To: Dave Ingram; Stephen Britt
Cc: Zimmerman, Darin; in...@list.soa.org
Subject: RE: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
Simple example which may help ?
Suppose in one years time I have a management charge due of 1% of an equity fund presently worth £1m.
Assuming a 5% risk-free rate and a 3% equity risk premium, my "real world" expected cashflow is £1m x 1% x (1 + 5% risk-free + 3% premium) = £10,800.
However unless this is hedged, I need to hold Economic Capital (EC) against a shortfall in the cashflow due to falling markets. Assume we need to set aside £5,000 now to cover a fall in equities in one years time at a certain confidence level (ca.50%) - at that time, the cost of that capital is 6% x £5,000 = £300.
The expected cashflow less the cost of capital gives £10,500 in one years time, and discounting this at the risk-free rate would give a present value of £10,000.
The risk-neutral and (one would hope) market consistent approach would be to roll up the fund at the risk-free rate, giving a cashflow of £10,500 in one-years time and a present value of this of £10,000.
Its a bit crude but I hope it illustrates that the two approaches should give the same result. I would also note that 6% is not set in stone but should be a function of the confidence level you choose for EC and by implication an organisation's target rating. The higher the rating, targeted the greater the EC buffer required but a higher rated entity should be able to raise capital more cheaply so its cost of capital should be lower. I also see a link between EC, the cost-of-capital and the equity risk premium you assume.
From: Dave Ingram [mailto:davei...@optonline.net]
Sent: 24 June 2010 00:46
To: Stephen Britt
Cc: Zimmerman, Darin; in...@list.soa.org
Subject: Re: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital method
The way that I like to think of it is that all risk should be included once and only once in the calculation. So either in the discount rate or in the cashflows. But not both.
I have had two questions about the cost of capital method:
1. Has anyone checked if it is even remotely close to what you get for a market traded risk? What I mean is if you deconstruct a market traded risk and solved for the market consistent COC that reproduces the price are there any examples that give an even slightly similar result?
2. This method makes the untraded risks on the balance sheet seem like the most stable things while the traded risks will bounce around as market based risk margins bounce up and down. I think that it send an exact backwards message about the desirability of traded vs. untraded risks.
So my suggestion would be to combine the two ideas and create an index of market implied COC that would be used to adjust the 6% standard COC up and down as the market gets more and less risk adverse. Otherwise the system seems to incent shifting into untraded risks whenever the market risk margins go up.
Dave Ingram
On Jun 23, 2010, at 6:01 PM, Stephen Britt wrote:
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.
There are a number of ways of getting at the' risk adjusted' value of a set of risky cash flows. Two of them are:
· Discount the expected cash flows at a risk adjusted discount rate; or
· Discount the risk adjusted cash flows at the risk free rate.
Generally in financial economics you do the latter - apply a change of measure / change probabilities to risk adjust the cash flows then discount at the risk free rate (then take an average). The CoC risk adjusts the cash flows more directly - by adding an explicit risk charge. The discount rate should still be the risk free rate, though.
Some other observations:
· This doesn't really 'solve the problem' though. It changes the question from 'what is the appropriate discount rate?' to 'what is the correct amount of capital to hold?';
· This method is not the preferred method in Australia (at this moment in time). For many years we have used a quantile approach to setting regulatory risk margins (this is a valid approach - just different. This may change over time, as it is not usually wise to be arbitrarily different;
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Frank Ashe
Dear Actuarial Colleagues:
In keeping with my training, early in my actuarial career I adhered o cost-of-capital thinking; at one point in the early 1990s I was the keeper and improver of NCCI’s IRR model for loading profit into WorkComp rates. However, by the mid 1990s I had realized the inconsistency of this thinking. Discounting expected cash flows and ROE on allocated capital are crude banking notions that do not serve insurance risks, which are instances of gambling. (Nor do they serve their purpose even in banking.)
Having presented the arguments many times in papers and at CAS presentations, I’m amazed that though bright actuaries, economists, and MBAs cannot answer my arguments, they continue to use these inconsistent methods. Time and again the emperor refuses to believe that he’s unclothed.
Please, let those of you to whom risk-adjusted discounting and cost of capital are problematic read brief portions of two of my papers:
1) Appendix A of “The Valuation of Stochastic Cash Flows,” CAS Forum (Spring 2003), www.casact.org/pubs/forum/03spforum/03spf001.pdf
2) “Valuing Stochastic Cash Flows: A Thought Experiment,” CAS Forum (Winter 2004), http://www.casact.org/pubs/forum/04wforum/04wf291.pdf
Eventually a Copernican revolution in finance will do away with RAD and CoC – actually Ptolomy’s epicycles, unlike today’s financial notions, were logically consistent. It took nearly 400 years for the Roman Catholic Church to admit that Galileo was right; I hope that the CoC church is less intransigent.
Sincerely,
Leigh
Leigh
Joseph Halliwell, FCAS,
MAAA
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Stephen Britt
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It’s not that complex, really. What confuses things is the rationale for the approach and its implementation in SII, not the method itself.
Assume I have a liability to pay out uncertain cash flows in future (say I’ve written motor insurance for many years and want to get out of insurance). You want to ‘buy’ this and I want to ‘sell’ it. So I am going to hand over a bunch of money to you then you have the responsibility to make the payments.
The first thing to do is to find out the market price of this proposed transaction. At what price did this arrangement (or an equivalent arrangement) trade previously, one nanosecond ago? I would be tempted to trade at the same price.
If there have been no cash flows then I ask ‘at what price would a willing but unforced seller (i.e. me) and a willing but unforced buyer (i.e. you) be willing to conduct this transaction? This is what SII want us to value the liability at in their statutory books.
How much would you have to be paid to accept the liability?
· If you received the expected value (at a risk free rate) of the cash flows then you could invest this sum in a risk free asset to match the expected cash flows. Good, but you have no reward for taking on the liability so you need to be paid a profit margin.
· This liability being risky you may need to set aside capital to meet the liability. The profit margin is the amount which, invested in the risk free asset, will provide your return on the capital you have allocated to this liability.
· The value you will accept to take on the liability is then the sum of:
o The present value (at the risk free rate) of the expected cash flows; plus
o The present value (at the risk free rate) of the emerging profit (allocated capital * Cost of Capital at each time period).
You will then take this amount, invest it in the risk free assets, and expect to receive your required return on the capital employed.
This is elegant, consistent with corporate finance and in some ways intuitive.
Steve.
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Sent: Sunday, 27 June 2010 7:20 PM
To: in...@list.soa.org
Subject: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital
method
Some further thoughts on this issue. The following seems to reflect the commonly held view:
There are a number of ways of getting at the’ risk adjusted’ value of a set of risky cash flows. Two of them are:
I Discount the expected cash flows at a risk adjusted discount rate; or
From: Dave Ingram [mailto:davei...@optonline.net]
Dave Ingram
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This E-Mail is confidential. Unauthorised recipients must notify the sender immediately on 0131-655-6789 and must delete the original E-Mail without taking a copy. We virus scan and monitor all e-mails but are not responsible for any damage caused by a virus or alteration or our email by a third party after transmission. The E-Mail is not intended nor should it be taken to create any legal relations, contractual or otherwise.
The following companies are part of the Scottish Widows Group and, with the exception of Scottish Widows Services Limited, are authorised and regulated by the Financial Services Authority. They are all registered in the United Kingdom:
Scottish Widows plc, Co No. 199549/FSA Register No. 191517; Scottish Widows Annuities Limited, Co No.199550/FSA Register No. 191518; Scottish Widows Services Limited, Co No.189975; Scottish Widows Unit Funds Limited, Co No. 74809/FSA Register No. 202648; all having their Registered Office at 69 Morrison Street, Edinburgh, EH3 8YF.
Scottish Widows Bank plc, Co No. 154554/FSA Register No. 201601. Registered Office at 67 Morrison Street, Edinburgh, EH3 8YJ.
Scottish Widows Unit Trust Managers Limited, Co No. 1629925/FSA Register Co No. 122129, Registered Office at Charlton Place, Andover, Hampshire SP10 1RE.
Scottish Widows Investment Partnership Limited, Co No. 794936/FSA Register Co No. 193707; SWIP Fund Management Limited, Co No. 406604/FSA Register No. 122135 and SWIP Multi-Manager Funds Limited, Co No. 5582499/FSA Register No. 455821; all having their Registered Office at 33 Old Broad Street, London EC2N 1HZ.
Scottish Widows Fund Management Limited, Co No. 74517/FSA Register No. 119359; Pensions Management (SWF) Limited, Co No. 45361/FSA Register No. 110422; all having their Registered Office at 15 Dalkeith Road, Edinburgh, EH16 5BU.
Lloyds TSB Investments Limited, Co No. 106723/FSA Register No. 122130, Registered Office at 60 Morrison Street, Edinburgh, EH3 8BE.
Scottish Widows Administration Services Limited, Co No. 1132760/FSA Register No. 139398, Registered Office at 25 Gresham Street, London, EC2V 7HN.
All of the above companies are part of the Lloyds Banking Group.
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Stephen Britt
Note: This e-mail is subject to the disclaimer contained at the bottom of this message.
BTW Hank, I don’t agree with your requirement 2. There is no forced inequality between quantum of risk margin and capital required. The quantum of risk margin is a one-off addition to a transaction which must support capital for the length of the investment. The risk margin is the present value of a series of cash flows. When money is cheap the risk margin will need to be higher.
Don’t confuse capital with claims paying capacity. Claims paying capacity is the sum of:
1. Present value of expected claims; plus
2. Risk margin; plus
3. Capital.
I see no reason for 3 to be greater than 2. They are linked, in that they should both increase with the riskiness of 1.
Steve.
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STEPHEN BRITT
SENIOR MANAGER
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INSURANCE AUSTRALIA GROUP (IAG)
T +61 (0)2 9292
2311
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From: Hans Waszink
[mailto:in...@waszinkadvice.com]
Sent: Sunday, 27 June 2010 7:20 PM
To: in...@list.soa.org
Subject: [Spam] RE: INARM Message - Risk Margin and the Cost of Capital
method
Some further thoughts on this issue. The following seems to reflect the commonly held view:
There are a number of ways of getting at the’ risk adjusted’ value of a set of risky cash flows. Two of them are:
I Discount the expected cash flows at a risk adjusted discount rate; or
From: Dave Ingram [mailto:davei...@optonline.net]
Dave Ingram
<HRsize=2 width="100%" align=center>
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As part of the Lloyds Banking Group, Scottish Widows is proud to be an Official Provider of the London 2012 Olympic and Paralympic Games. www.scottishwidows.co.uk/london2012
This E-Mail is confidential. Unauthorised recipients must notify the sender immediately on 0131-655-6789 and must delete the original E-Mail without taking a copy. We virus scan and monitor all e-mails but are not responsible for any damage caused by a virus or alteration or our email by a third party after transmission. The E-Mail is not intended nor should it be taken to create any legal relations, contractual or otherwise.
The following companies are part of the Scottish Widows Group and, with the exception of Scottish Widows Services Limited, are authorised and regulated by the Financial Services Authority. They are all registered in the United Kingdom:
Scottish Widows plc, Co No. 199549/FSA Register No. 191517; Scottish Widows Annuities Limited, Co No.199550/FSA Register No. 191518; Scottish Widows Services Limited, Co No.189975; Scottish Widows Unit Funds Limited, Co No. 74809/FSA Register No. 202648; all having their Registered Office at 69 Morrison Street, Edinburgh, EH3 8YF.
Scottish Widows Bank plc, Co No. 154554/FSA Register No. 201601. Registered Office at 67 Morrison Street, Edinburgh, EH3 8YJ.
Scottish Widows Unit Trust Managers Limited, Co No. 1629925/FSA Register Co No. 122129, Registered Office at Charlton Place, Andover, Hampshire SP10 1RE.
Scottish Widows Investment Partnership Limited, Co No. 794936/FSA Register Co No. 193707; SWIP Fund Management Limited, Co No. 406604/FSA Register No. 122135 and SWIP Multi-Manager Funds Limited, Co No. 5582499/FSA Register No. 455821; all having their Registered Office at 33 Old Broad Street, London EC2N 1HZ.
Scottish Widows Fund Management Limited, Co No. 74517/FSA Register No. 119359; Pensions Management (SWF) Limited, Co No. 45361/FSA Register No. 110422; all having their Registered Office at 15 Dalkeith Road, Edinburgh, EH16 5BU.
Lloyds TSB Investments Limited, Co No. 106723/FSA Register No. 122130, Registered Office at 60 Morrison Street, Edinburgh, EH3 8BE.
Scottish Widows Administration Services Limited, Co No. 1132760/FSA Register No. 139398, Registered Office at 25 Gresham Street, London, EC2V 7HN.
All of the above companies are part of the Lloyds Banking Group.
*******************************************************************************
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