Monday, April 18, 2011

MPT gives thumbs up to Garth Turner

As I noted in my last post, Stephen Gordon has got it right on corporate taxation. Unfortunately he has it wrong, however, when he calls for former MP and financial advice blogger Garth Turner to be corrected with "the math."

I won't say that Garth's latest morsel of financial advice is "right" in all its details, never mind that he's right about the "goal of life" (the grand title of Garth's latest post) being related to achieving some level of financial wealth. But I can say that Dr Gordon is the mistaken party when he says that "variances and covariances and CAPM and stuff" will expose the errors of the former Parliamentarian.

In the comments to Gordon's post, Andy Harless takes a stab at "the math" by offering an example of how adding an asset that is less than fully correlated reduces the variance of a portfolio. In the world of "modern portfolio theory" or MPT, variance and risk are one and the same; a dubious assumption in my view but one I'll just run with for the purposes of this post. So far so so good. But then Dr Harless says, "Now free up a and b so that you can use leverage, i.e., take away the constraint that a+b=1." Sorry, but one cannot take away the constraint that the coefficients add up to 1 without taking away the equation. A weighted average means the coefficients must sum to 1 by definition.

When Garth suggests that people who have a $400K portfolio consisting solely of a house take out a home equity line of credit secured against the house for $200K and use the money for investing in a variety of other assets like financial instruments, he is indeed recommending diversification. The former portfolio contained a sole asset, the house (we'll call this asset X), and its weight coefficient was 100%, ie a = 1. In the new portfolio, a is still 1 ($400K) while the coefficient (say, "b") of the new assets (which we'll call asset Y) is 0.5 ($200K) and the coefficient (say, "c") of the HELOC (asset Z) is -0.5. The coefficient for the loan is negative because one is short the security. Thus a + b + c = 1 + 0.5 - 0.5 = 1.

Since variance is the square of standard deviation ("σ"), the variance of the portfolio is given by

where the CORR functions are the correlations between the subscripted terms (e.g. the first CORR term is the correlation between asset X and asset Y). Now suppose the standard deviation for asset X is 5% and 10% for asset Y, while the expected returns are 4% and 8% respectively. This would mean the house is expected to appreciate at just half the average annual rate of the new assets excluding the loan, but with just half of the volatility as well. Let's also assume the correlation between X and Y is 0.5. The standard deviation of asset Z would be zero if it's deemed a risk-free asset, which is an important concept in MPT. A risk-free asset returns the risk-free rate, which we will assume to be 3% for this example. The loan here may be reasonably defined as risk-free because it is secured by the home: the lender is accordingly guaranteed to be paid. As noted earlier, MPT defines risk as being variance, so the standard deviation of Z is zero.

Plugging these numbers in means the deviation for the new portfolio is 8.66%:

So Stephen Gordon is correct that total risk has been increased. A standard deviation of 8.66% is higher than 5%, which was the house alone. But can it be said conclusively that Garth Turner has "not got it right"? No, because the expected rate of return is also higher, and not just higher, but would be higher after adjusting for the increased risk. MPT uses what's called the Sharpe ratio to measure excess return per unit of risk. It subtracts the risk-free rate from the portfolio's expected return and then divides that by the portfolio's standard deviation. The portfolio's expected return is simply the weighted average of the expected return on its components, ie:

Another way to calculate this would be to take the dollar value of the expected return on the house (4% of $400K or $16K), add the additional $16K one would expect on the $200K investment (that returns 8% per annum), subtract the $6K one would have to pay on the $200K HELOC, and divide the resulting $26K by one's $400K net equity interest in the new portfolio. The Sharpe ratio for the new portfolio is 6.5% - 3% divided by 8.66% or 0.404. For the old portfolio of the house alone the Sharpe ratio was 4% - 3% divided by 5% or 0.2. In sum, while Garth's recommendation does increase risk, it more than compensates in higher expected return.

Now someone may object that the particular numbers I chose produced this result. Before one quibbles too much about that, I could make some observations about some of them such as noting as Garth does that the interest paid on the HELOC is tax deductible because it is considered money borrowed to invest and the investment is not in a tax-shelter. But the full answer is that the proposal is well-founded as a matter of theory and what I've provided is just an example.

MPT is primarily concerned with building mean-variance efficient portfolios. This means finding a portfolio mix on the "efficient frontier." Graphically, the efficient frontier (for a portfolio not including a risk-free asset) can be represented by the left boundary of a hyperbola sometimes called the "Markowitz bullet." One can think of the individual points along the frontier as portfolios of different risky assets in different proportions. The addition of a risk-free asset to the portfolio creates a new efficient frontier called the Capital Asset Line - or Capital Market Line (CML), which is the best possible Capital Asset Line - tangent to the hyperbola at the point where the Sharpe ratio is highest. Shorting the risk-free asset, or using leverage, is represented by the line above this point, which I have indicated in red:

Call the red part of the line the "Garth zone," if you like. All points on the CML have the maximum Sharpe ratio. It shows that just adding cash to a portfolio (represented by the part of the CML that is not red) or deleveraging can improve expected return for a given level of variance just as leverage can.

There are, of course, problems with this model like the fact it assumes that the variance of the assets has a neatly defined probability distribution. But almost all financial models have this problem, which can be loosely described as the "fat tails" problem. Garth Turner is in any case right in a more general sense in my view, since he appreciates the fact that the people who become truly wealthy in their own right through investments almost always use leverage to get there. Garth sums up, "The holy grail isn’t living in a place your friends covet. Then they’re not friends. The object is to posses enough wealth with liquidity to give you options. Freedom, choices." I think this is sound observation; a big house just ties one down, such that what the former Liberal (and former Conservative) politician proposes provides not just diversification benefits but liquidity benefits.

Wednesday, April 13, 2011

off-balance sheet government

Were the current federal election campaign to come and go without my blogging about it, this blog would surely be given up for dead completely. Hence a few "observations."

My objection to the Harper Conservatives that they aren't really conservative remains, but it is interesting that more of the policy community is cottoning on to how narrow "tax cuts" are actually social programs dressed up at please the smaller government crowd. The centrist Brookings Institute recently hosted a panel discussion on the topic that follows up what Greg Mankiw and other economists having been saying. This afternoon President Obama called for cutting a trillion dollars worth of "tax expenditures", a cut the Republicans will of course describe as a tax hike.

The Tories' March budget continued to fragment the tax code, and the one big dollar proposal the Tories have made to date as a campaign promise, which is to allow more income splitting between couples (after the deficit has been eliminated), continues in that vein.

Income splitting is a broader tax break than most of the other extremely narrowly targeted tax breaks the government has offered, but it is still selective. What matters here is that this revenue loss comes at the opportunity cost of providing tax relief to everyone. What is the economic rationale for not providing relief to individuals as well? What social or equality objective rationale is served by a policy that does nothing for families headed by single mothers? The short answer of course is that it serves a political objective: getting credit for proposing a "tax credit" but then restricting its cost by narrowing its application.

Want to give a handout to an influential interest group but avoid "conservative" ire at your spending? Ask your staff to investigate the nature of that group's tax liability and then structure the handout so as to reduce that liability as opposed to an overt subsidy. Gives the group the same benefit while nominally keeping the "size of government" limited. One can call it moving government off-balance sheet, because although the the size of government is nominally limited, it has still interfered in the allocation of resources across the economy. What does it mean to be an economic "conservative", if not to prefer private markets over central planning?

Aside from this, there's the more obviously non-conservative policies espoused by the Harper regime, like attacking the Liberals for not standing as strongly behind trade barriers (e.g. noting that the “Liberal Party’s platform makes no mention of supply management.”) This is the same supply management, of course, that Harper denounced as "government-sponsored price-fixing cartels" when he was a private citizen instead of a politician.

The Harper government is simply too hostile to complex policy for those who appreciate the need for such complexity for someone like myself to not conclude that working for or supporting them would not be prohibitively frustrating.

In 2008, instead of sending a new Tory backbencher with a legal cloud over his head to Ottawa to represent Edmonton-Sherwood Park, a voter like myself could check off the Liberal candidate and send a PhD in Economics to Ottawa to represent the riding and support a Liberal platform that called for a targeted tax with a sound economic rationale. Although the "Green Shift" was somewhat corrupted as a policy plank, it still aimed to discourage production that created a negative (or possibly negative, which is the minimum that can be said about carbon emissions) externality.

2011 is somewhat different. The Tory attitude in general has hardly changed - consider the statement of Harper's former Chief of Staff that "Politically it helped us tremendously to be attacked by this coalition of university types." But the Conservatives are actually on the right side of the issue with respect to corporate tax cuts, and it appears that this idea was actually allowed to escape from the non-partisan Department of Finance as opposed to being hatched, like most Tory policies, in the brain of a Conservative "strategist"/poller.

I won't repeat all the arguments for a cut in the general corporate rate. Stephen Gordon (photo at right from Laval University), has been making valuable contributions on the Globe and Mail's website that have served as a corrective to some of the claims of labour economists as the topic has developed as a political issue. I say labour economists instead of "progressive" economists because for those who are not on a union payroll, I believe a full analysis would lead them to agree with Laura D'Andrea Tyson, who notes on the NY Times website that "a high corporate tax rate... is also increasingly ineffective as a tool to achieve more progressive outcomes..." Most astute observers understand what the preponderance of evidence and argument supports.

Toronto Star columnist James Travers (photo below) passed away on March 3 and, in keeping with the Star's political lean, was a fierce critic of the Harper regime. Travers nonetheless understood that several "conservative" principles like free trade are well justified. Travers' February 8 column neatly summed the politics of the corporate tax cut issue:
Caught on the slippery slope of a popular proposition, Harper and Finance Minister Jim Flaherty are appealing to voter’s cerebral side. Aided and abetted by conservative economists, they’re constructing the analytical case that corporate tax cuts will pay dividends in jobs as well as productivity and won’t cost the federal treasury the $6 billion annually that critics claim.
Watching Conservatives slip and slide trying to push a policy rock uphill is a delicious treat for political rivals, deputy ministers and egghead academics.
For five years now they have been struggling against the ruling party’s populist gravity. ...

In my view, Michael Ignatieff's run to the left wasn't just bad policy but bad politics. Jack Layton is not about to be snookered at his own game of appealing to the anti-"corporate agenda" crowd. The Tories created all sorts of space for an opposition campaign that indicated that it would stay the course economically (or got even more aggressive on deficit reduction) but attacked the government for its contempt for Parliament and its contempt for "university types" in general, which manifests itself in things like manipulating the census, something that disturbed many swing voters. Instead the Liberals have tried to appeal to NDP voters, which is only going to be as effective as Jack Layton allows it to be. Judging from last night's TV debates, I don't think Layton lost any people to Ignatieff, meaning Ignatieff will likely end up ruing the decision to focus on the Liberal/NDP swing vote instead of the Liberal/Conservative swing vote.