Arbitrage worksheet

[Jeremy Gold]

The worksheet that supports Chapter 4 of the Pension Actuary's Guide to Financial Economics has been posted:

http://new.soa.org/professional-inte...sArbitrage.xls

Feedback is welcome.

Edited to update worksheet address -- for best results save worksheet on your computer and open with excel; may not work as well if you open in your browser.

[Single White Shemale]

Originally Posted by Jeremy Gold

The worksheet that supports Chapter 4 of the Pension Actuary's Guide to Financial Economics has been posted:

http://www.soa.org/ccm/content/areas...nce-resources/

Feedback is welcome.

Which version of Excel is your worksheet compatible? Will it work with Excel95?

[Duffer]

Driving a 12 year old car is safer than 12 year old software.
I vote for upgrading your version.

[mark007]

Pushing bonds again I see. In the interest of debate, I wonder if you have any thoughts on this article:

http://www.the-actuary.org.uk/pdfs/07_03_02.pdf

[PaulConrad]

Originally Posted by mark007

Pushing bonds again I see. In the interest of debate, I wonder if you have any thoughts on this article:

http://www.the-actuary.org.uk/pdfs/07_03_02.pdf

That used to be true when written (some time before March 2007), but once the market realized that equities were a superior long term investment, the price of equities adjusted such that the return was reduced and bonds again became attractive as no new articles have come out yet to stem the overbuying of equities.

[Jeremy Gold]

Originally Posted by mark007

Pushing bonds again I see. In the interest of debate, I wonder if you have any thoughts on this article:

http://www.the-actuary.org.uk/pdfs/07_03_02.pdf

The Actuary should be embarrassed to publish such an article in 2007. In the past, I have responded to Cass professors in the Actuary. By now I have lost patience with the Actuary. I will let you Brits rebut the endless Cass output. (Not all Cass professors are created equal, but several in the actuarial department appear to be better mathematicians than they are economists.)

The Pension Actuary's Guide to Financial Economics, in a chapter preceding the explanation of the spreadsheet makes the critical distinction between individuals (who balance risk and reward in order to maximize their expected utilities) and institutions which must accept the market price of risk and maximize value (properly discounted for risk). In this context I use the term institution to describe widely held institutions like publicly traded corporations and institutions like state government pension plans which have wide taxpayer bases. Closely held insitutions may have some justification for behaving like indidivudals.

As an individual, I have recently reduced my equity exposure from 94% to 79%. Oh yeah, I believe in the ERP and invest to capture as much of it as I can, given my limited risk tolerance. If not for liquidity needs, all of my 21% not in equity would be in tax sheltered savings.

Anyone who wants to continue the debate owes it to me to read the Actuary's Guide before asking me to defend it. Here too, Mark, your Britishness buys you a little room. You probably did not, as all members of the SOA Pension Section (which you are welcome to join) did, receive a free copy. So spend the 15 bucks, make the SOA happy, and read it.

Although I no longer owe explanations of the bond/equity debate to actuaries with access to the Guide who have not read it, you owe it to yourself and your future to master the arguments, even if you disagree and even if your mastery is merely the prelude to an effort to continue the debate.

Oh yeah, I am jetlagged and crotchety at the moment, so I hope I have only offended those few who deserve to be offended.

[WWSituation]

Originally Posted by PaulConrad

That used to be true when written (some time before March 2007), but once the market realized that equities were a superior long term investment, the price of equities adjusted such that the return was reduced and bonds again became attractive as no new articles have come out yet to stem the overbuying of equities.

I'm guessing this is sarcasm. I thought we were ok about the fact that adding equities to a pension's portfolio adds zero value to the sponsoring company.

[mark007]

Oh yeah, I am jetlagged and crotchety at the moment, so I hope I have only offended those few who deserve to be offended.

No offence taken (provided I am not in the few). Your post was surprisingly polite (surprising in that many others here have taken the sacrcasm route rather than actually answering anything when this has been discussed in the past, rather than it being surprising that you are polite!)

Although not jet lagged I am certainly baby lagged so I apologise if I make any school boy errors!

Before I continue, is there anything new in the Pension Actuary's guide (that's not in Andrew Turner's paper in 2004 for example)? If so, then in the spirit of international debate please feel free to send me a copy.

I have to say that to some extent I have been swayed by the bonds argument in the past - it all follows fairly logically. I even presented the ideas to colleagues as part of an internal "actuarial day".

If I consider the arguments I would have to say that the main reason companies don't invest in bonds is due to agency costs. However, I think there are also some key human behaviour aspects and utility ideas that also muddy the waters a little.

I have to say though, and you clearly agree, that equities are the best investment over the long-term. The debate therefore seems to come down not to whether equities are the best long-term real asset to hold but whether they are the best asset for a pension fund to hold.

I have actually responded to the article in the Actuary, but not in the vein that I am sure you would have done. For although I (on the whole) agree with the article, I find it difficult to argue that the short-term volatility of equities can be tolerated for all but the very, very strong companies due to the very real risk that the liabilities are actually short-term due to insolvency. By very, very strong I therefore mean a company that could easily afford to put a cash injection of say 30% of the value of the assets into the fund in any year. From a regulation and Trustee perspective it therefore seems difficult to me to recommend equities. The only exception being if there was a national pension shortfall fund that covered 100% of the benefits and also invested in equities.

I imagine on the other hand that your approach would be that of tax arbitrage increasing shareholder value by investing in bonds.

Thinking about this now I have the following thoughts:

1. The argument hinges on the increased risk of equities offsetting the expected cost savings. Something I'm not sure I agree with when you have investors with different time horizons etc. (this was touched on in the article in the actuary)

2. Not only would companies argue that investing in equities saves on pension costs but they would also argue that the money saved could be invested in the company and generate double digit returns.

3. If I am the sole shareholder and MD of a company with a DB pension scheme then I expect that by investing in equities my pension costs will be reduced thus increasing my profits and dividends. I don't care what the company is valued at as I'm not looking to sell. Would you be suggesting I should sell a large proportion of my company, invest the DB scheme assets in bonds and purchase risky shares in companies I have no control over in industries I don't understand up to my risk tolerance?

Overall, I think the FE risk free world, no arbitrage, no transaction costs, same time horizons etc. is as over simplifucation of the real world. I think all bonds strategies have a place in many companies and FE aside I think there are strong covenant arguments to put forward the case for investing in bonds. However, ignoring the covenant issue (from a commercial angle as we'd get sacked if this was always the recommendation! (this is something that would have to be doen through regulation)) there are still companies for which a significant equity holding is valid, particularly those up *** creek without a paddle and small companies. I think that in the end the best strategy is neither all bonds nor all equities but a diversified portfolio of equities (domestic and overseas), bonds (gov't and corp.), property and some derivatives and swaps (particularly credit and currency) along with other more complicated investments.

[Stuart Jarvis]

Originally Posted by mark007

I have to say though, and you clearly agree, that equities are the best investment over the long-term. The debate therefore seems to come down not to whether equities are the best long-term real asset to hold but whether they are the best asset for a pension fund to hold.



I have actually responded to the article in the Actuary, but not in the vein that I am sure you would have done. For although I (on the whole) agree with the article, I find it difficult to argue that the short-term volatility of equities can be tolerated for all but the very, very strong companies due to the very real risk that the liabilities are actually short-term due to insolvency. By very, very strong I therefore mean a company that could easily afford to put a cash injection of say 30% of the value of the assets into the fund in any year. From a regulation and Trustee perspective it therefore seems difficult to me to recommend equities. The only exception being if there was a national pension shortfall fund that covered 100% of the benefits and also invested in equities.

I imagine on the other hand that your approach would be that of tax arbitrage increasing shareholder value by investing in bonds.

Thinking about this now I have the following thoughts:

1. The argument hinges on the increased risk of equities offsetting the expected cost savings. Something I'm not sure I agree with when you have investors with different time horizons etc. (this was touched on in the article in the actuary)

2. Not only would companies argue that investing in equities saves on pension costs but they would also argue that the money saved could be invested in the company and generate double digit returns.

3. If I am the sole shareholder and MD of a company with a DB pension scheme then I expect that by investing in equities my pension costs will be reduced thus increasing my profits and dividends. I don't care what the company is valued at as I'm not looking to sell. Would you be suggesting I should sell a large proportion of my company, invest the DB scheme assets in bonds and purchase risky shares in companies I have no control over in industries I don't understand up to my risk tolerance?

Overall, I think the FE risk free world, no arbitrage, no transaction costs, same time horizons etc. is as over simplifucation of the real world. I think all bonds strategies have a place in many companies and FE aside I think there are strong covenant arguments to put forward the case for investing in bonds. However, ignoring the covenant issue (from a commercial angle as we'd get sacked if this was always the recommendation! (this is something that would have to be doen through regulation)) there are still companies for which a significant equity holding is valid, particularly those up *** creek without a paddle and small companies. I think that in the end the best strategy is neither all bonds nor all equities but a diversified portfolio of equities (domestic and overseas), bonds (gov't and corp.), property and some derivatives and swaps (particularly credit and currency) along with other more complicated investments.

Confused about your three points here

1) You are framing this in terms of a risk / return trade off (equity volatility v "cost savings") rather than in terms of value of the firm. See Jeremy's earlier post about the appopriate decision framework here (corporate finance rather than personal finance).

2) This is a valid comparison but suggests to me the opposite conclusion. Surely a company should spend its capital on these internal risky projects rather than on other companies' risky projects? I think the confusion arises from an implicit and inappropriate pre-booking of the equity risk premium.

3) Again, yes, if equities are such a tremendous one-way bet then you should pack up everything else you're doing and invest in equities. But this is clearly dumb and ignores the risk that is being priced by the market.

Your final points are right I think: consultants' self-interest necessarly impacts on the advice being given to pension plans; it's much easier to say that plans should spread their asset risks across multiple asset classes, than to give more crunchy advice that takes into account the liabilities and the wider interests of the firm.

[mark007]

To clarify then:

1. The value to the firm you are talking about comes from tax arbitrage and only works provided there is no difference in value of a company that has a bond investment and one that has and equity investment. This should clearly be the case but I'm not convinced it is, due to the focus on earnings.

2. It certainly should and it would have more capital to do so by investing in equities. Note that whether the expected outperformance should be allowed for in advance is another debate altogether (one in which I would favour making an allowance) but it doesn't fundamentally effect the fact that in the long-term the scheme will require less capital.

3. I think you have mis-understood. In this example I am not making a personal investment in equities but have built a company that I own. Having said that I do believe that over the long-term equities are a great bet as has been agreed.

Self-interest certainly affects the advice given. Howevre it is only advice and provided the advice covers all angles, which it normally does, then it is up to someone else to make the decision. However if an all bonds strategy is so good for the firm then providing this advice would be exactly what the company wanted to hear! It isn't though. So really it comes down to an agency cost i.e. the directors being interested in their own interests rather than shareholders. Even then it comes down to shareholders who are too focused on earnings and so set earnings reakted targets and bonuses. The sea change if there is to be one has to start at that level.

Alternatively there are flaws in the arguments made for an all bonds strategy. Personally I think there are some flaws. For example I could buy insurance to cover me for all possible losses I could ever have. I don't though because then I wouldn't have enough money to live my life the way I want. Investing in bonds is like purchasing some form of insurance but it restricts the cashflow of the company. There may be eventual tax savings to individuals who invest in the company but at what cost.