IRR and Returns on Portfolios

There is a very interesting discussion at the Canadian Capitalist’s blog about how to determine performance and there was some talk of Internal Rates of Return (IRR):

In one comment, the Canadian Capitalist, said:

It is true that IRR is the true measure of performance but what I did in my earlier post was compare the IRR of my actual portfolios with the annual return of the benchmark (to which no money was added). That is really comparing apples to oranges.

He is referring to the fact that is benchmark sleepy portfolio earned 14.7% last year vs. a 9.55% annualized return (for last year) for his own portfolio.

I have a reply to that that is kind of long so I thought I’d post it here:

I think it is ok to compare your porfolio’s IRR to the annual rate of return of the benchmark. I went back to the definition of IRR since I had sort of lost track of what it really mean, and this sentence sort of brought it home for me:

IRRs can also be compared against prevailing rates of return in the securities market. If a firm can’t find any projects with IRRs greater than the returns that can be generated in the financial markets, it may simply choose to invest its retained earnings into the market.

When companies do this, they are comparing some IRR calculated with some complex set of cashflows to the prevailing annual rate of return in the market. The benchmark’s annual return is an IRR too, there is just one cashflow in, one cashflow out.

Essentially what I think happened with the CC’s portfolio is that his further purchases during the year were at (relatively-speaking) high points in the market. And the IRR comparison to the annual return of the index is correct. He had a worse return than someone investing all of their money in the index at the beginning of the year did.

But, the bigger/better question is, would he have done better had he put his cashflows throughout the year into the index/(or in his case, the sleepy portfolio). Well it depends on timing and what happened in the market but I think an IRR calculated from those cashflows might be interesting, because it would show how well he would have done had he invested in his benchmark portfolio instead of his real portfolio. So the IRR really can show you how well you did by revealing bad timing and such.

I just did the XIRR calculation on a spreadsheet to check this…but it looks like if we were comparing an IRR of a portfolio made up of purchases of an index ETF made throughout the year, let’s say, and the daily return was the same for every day of the year, the IRR of your portfolio would match the annual return of the index exactly. So I think it might be true that in the limit of a linearly increasing/decreasing market/investment, the annual return is equal to the IRR of any cashflows invested in that market/investment.

No time to look this over or spellcheck this, so I’m sorry, but I’m really busy!

Monte Carlo Investment Simulation

Many months ago, I saw this blog post about a Monte Carlo investment simulator. I liked it right off the bat because rather than giving exact answers, it gives probabilities of outcomes instead. You can read more about Monte Carlo method at Wikipedia.

A few comments about their simulator:

  • At first I was annoyed that I couldn’t specify my estimated nominal return on my investments. But then I thought, well, they have probably determined the average return of a conservative portfolio over the past few decades and so its probably better that I don’t have the power to change it, otherwise, I might be prone to use an overly-optimisted return
  • They use 4.83% as an expected inflation rate, which “corresponds to the average inflation rate for the period of 1974 to 2004” according to their instructions on their website. Isn’t that a bit high? The most I have ever heard quoted is 3-4%, but almost 5%?
  • I noticed that there is no way to specify a monthly cash flow into an asset. It turns out that any leftover surplus in the cash-flows tab will get transferred into assets (in the same proportion I assume).

I have been playing around with it for a while today and I plan on fine-tuning it a bit more. There are also a few other simulators that the blog post above mentions. Not sure how many of those are free though.

Investment Performance Software

I am in the process of writing some software that will allow me to input the current market values of my investments every month according to my monthly statement and see the annualized performance over any period I want for any of all of my investments at a time, but it is slow-going. What is the difference between this and Quicken or Microsoft Money? Well first of all, it is free. What is the difference between free programs like Gnucash, etc…? Those programs cannot do this kind of thing in the way I want to just yet. The main difference in usage is that all you need to do is enter information from your monthly statements, such as current market values of your investments and your investment transactions as well. Then various annualized returns can be calculated from that for all your investments, or the aggregation of all your investments over time (for example). It explictly does not rely on daily prices of anything. That is to promote sound conservative investment practice: that daily fluctuations in the market do not matter. If I can get all that to work in a framework that is flexible then I should be able to do a lot more with it too. If anyone things this is interesting or thinks that I am re-inventing the wheel, please tell me.


This article, “Cramer Google-Coaster (GOOG)” lists Cramer’s recent recommendations on Google stock:

January 3……….Buy…….$435.23 (going to $500)
January 4……….Buy…….$445.24 (going to $500)
January 13……..Buy…….$466.25 (going to $600)
January 23……..Buy…….$427.50
January 25……..Buy…….$433.00 (take profits)
February 2……..Buy…….$396.04
February 6……..Sell.. ….$385.10 (sell at $400)
February 14……Buy…….$343.32
February 27……Buy…….$390.38 (going to $500)
March 6………….Sell…….$368.10 (going down $15)
March 7………….Buy…….$364.45
March 13………..Sell…….$337.06
March 21………..Sell…….$339.92
March 23………..Buy…….$341.89
March 29………..Sell…….$394.98

I plugged them into Excel and set up some cash flows according to the following rules: purchase 100 shares of GOOG every time Cramer calls “Buy” and sell of half of the shares you own every time he calls “Sell.” I then used Excel’s XIRR function to determine the Internal Rate of Return, and got a -66% annualized return. Way to go Cramer. If you’d just bought 100 shares of Google on January 3rd and held it until March 29, you would have achieved a -34% annualized return. If you had of instead bought 100 shares of Google on all the dates above in order to dollar-cost average, you would have achieved an 8% annualized return by March 29th.

The analysts are always full of crap with their buy/sell recommendations and I am sure any reader of this blog is aware of that. What is sad is that Cramer’s show is insanely popular. What is even more sad is that a friend of mine’s dad is an investment advisor and he watches Cramer every day after work AND TAKES NOTES. To give him the benefit of the doubt, maybe he just watches the show and gambles 5% of his portfolio (his “mad money”) on some of Cramer’s picks. But still, I would not be happy if I suddenly found out my advisor watched Mad Money every day after work. I am extremely happy that I am not going to this person for financial advice/management. And I was very impressed when I first met my current advisor and he told me that he “does not pick stocks.” Nor does he sound like someone who would pay any attention to stock picks he heard on TV.

I only saw Cramer’s Mad Money once while in Hawaii (my only chance to watch the 24/7 American “news” stations). I think I watched for all of about 2 minutes until I dismissed it as crap and shut it off. Once in a while I hear about this Mad Money show. I remember Arrested Development poked fun at it and a little while back a stock recommendation on his show apparently caused Zarlink stock to increase 20% in one day.

Here are couple of comments on Cramer from “Ego Unleashed, or Everyman of the Market?“:

“What you are seeing when you watch that show is both a parlor game and real brilliance,” Mr. Bogle said. “But I think that when the final score is written, his return is very average, and below average when you factor in the costs of making the trades. We know that when you own the stock market and never trade, you will capture the market’s return. The more we trade, the greater the costs and the greater the loss. These are relentless truths that cannot be avoided.” [emphasis mine]

Another good article here: “Monitoring the ‘Mad Money’ Madness” by the Big Picture‘s Barry Ritholtz.

Air Miles Calculations

I did some annoying Air Miles calculations tonight. We are planning a trip to Cuba and we are trying to determine whether it makes sense to use our Air Miles or not. There are many annoying little details to think about. Since all Air Canada flights from Vancouver (YVR) to Havana, Cuba (HAV) are routed through Toronto (YYZ) (at least through Toronto, sometimes other cities as well) there are 3 options to consider: 1) using Air Miles for the YVR->HAV route, 2) the YVR->YYZ route, or 3) the YYZ->HAV route and obviously paying full price for whatever route is not covered by Air Miles in options 2) and 3). Also, because of the number of miles we have, some of these options work for both people, others work for only for one person. In some scenarios, our miles aren’t quite enough to meet the requirement but extra miles can be purchased for $0.30 + GST per mile. Also, I wanted to take into account the value of the remaining Air Miles (if any) associated with any of the scenarios. Also note that Air Miles only covers the base cost of the flight, not the fees (at least according to the lady I talked to on the phone).

Initially I ended up valuing the Air Miles at a very low price. I was valuing them according to what flights YVR-YYZ or YVR->HAV or YYZ->HAV were costing me in miles (works out to a valuation of $0.11-0.16/mile). But if we do have leftover miles after this trip we most likely will not be using them on those routes. My wife has a friend in Calgary and a flight there is likely in the near future so I checked how much miles were worth on that route. They are worth much more, at $0.23/mile. Also, the next time we fly anywhere (if at all) will be in November when we will take the rest of our vacation days. November is considered low season and a mile gets you much further at that time of year (on some routes the value of a mile goes from $0.11/mile to $0.16/mile). So I ended up assuming leftover miles were worth $0.16/mile. Here are the results:

Vancouver to Havana Air Miles Scenario Calculator

Well it’s not really that illuminating. The cases which split the flight into two segments are bad deals all-around because the split flights are a lot more compared to the single round-trip flight for YVR<->HAV. The “without Air Miles” option is better because I have valued the leftover air miles at $0.16/mile which is higher than the cost of using them for that YVR<->HAV flight. If I value the leftover miles at $0.11/mile the gap between the “without using Air Miles” option and the “Using Air Miles to HAV for 1” option becomes less than $100. That is something I am willing to pay in order to save the $638 on one of the flights now ($638=$808 base price of flight minus cost of lacking miles of $170) leaving more money in our pockets (or savings account, rather).

The other advantage of this is that using our Air Miles fully will bring our balance down to 0. I like that because it means we will not have any significant balance leftover in our Air Miles account. I am seriously considering getting rid of Air Miles account. The 10 years (yes I have been a collector since 1996 and have only redeemed once, for 750) it took me to get 7750 miles was not worth the hassle and I do not want any Miles hanging around in my account.

Should You Borrow To Invest in Your RRSP?

Many Canadians wonder whether or not they should borrow money to help them maximize their RRSP contributions. Never was this idea touted more than in 2002 onward when interest rates were very low. There is no reason why it is not a good idea now, and interest rates are still historically low. This article, “Should clients borrow to catch up on RRSPs this year?” discusses why it can be a good idea.

Even though many experts discourage the use of long-term RRSP loans, most people would actually benefit from them, claims Talbot Stevens, a London-based financial educator, author, and industry consultant.

“If you just look at the math, RRSP catch-up loans always make sense when investment returns match or exceed the cost of borrowing,” explains Stevens. “If you can borrow at 6% interest and get returns of 6% or higher, you will come out ahead by borrowing to catch up on RRSPs, even if it takes 10 years or more to repay the remaining balance of the loan.

He does not go into detail here but the math is fairly simple. If the return in your RRSP matched the interest on the loan, the amount the RRSP increased by in the first year would match the amount you owed in interest on the loan. Once you take into account the tax refund that will be generated due to the RRSP deduction (at your marginal tax rate multipled by the amount of the deduction) you can see that you will wind up ahead. But I am neglecting something. We will be taxed on the RRSP’s returns later, when we withdraw it. This will reduce our effective return inside the RRSP. Not only that but we will be taxed on the contributions we made as well. The math does get a bit complicated, and it is always made even more difficult by the fact that it is impossible to predict future returns on an investment inside an RRSP. As the author of the quoted article says, however, behavioural factors are often overlooked when considering the advantages and disadvantages of borrowing to invest in your RRSP:

Stevens also likes the investment discipline afforded by long term RRSP loans. “When you also account for the behavioural reality that most investors spend their RRSP refunds, the scales tip heavily in favour of long-term RRSP loans, even when returns are half of the cost of borrowing,” says Stevens.

“For most investors, the catch-up RRSP strategy generally produces a larger retirement fund because the loan locks in a higher level of commitment. Once started, the loan becomes a forced savings plan, like a mortgage, where we don’t have a choice but to continue the payments.”

At first I did not understand what “the behavioural reality that most investors spend their RRSP refunds” had to do with the scales tipping “heavily in favour of long-term RRSP loans.” I think what he means is that if you have a long-term RRSP loan, you will be less-inclined to spend (in other words, waste) your RRSP refund. Instead you will be more likely to put it down towards the loan in an effort to lower interest payments and/or get rid of the debt sooner. Of couse it is better to contribute to your RRSP with cold-hard cash, but if you cannot maximize your contributions with cash, there does not seem to be anything fundamentally wrong with getting an RRSP “catch-up” loan.

Of course most of the arguments for and against borrowing to invest in your RRSP also apply to the pay down your debt vs. contribute to your RRSP argument.

Incorrect Mutual Fund Charting On My Site

I was just looking at a chart today at Yahoo that did not make any sense. The chart compares Fidelity Low-Priced Stock Fund (FLPSX) with Legg Mason Value Trust (LMVTX). The problem is that over this period the former should have beaten the latter by a significant margin. According to this article at which I have referenced twice already, FLPSX had an 18.4% annualized return vs. 16.55% for LMVTX. Either the Yahoo chart is incorrect or the Forbes article is incorrect. Then it dawned on me, Yahoo is obviously just plotting the NAV which doesn’t take into account distributions! I found an article, “A Call for Decent Fund Charting,” that cleared things up for me.

Morningstar is apparently the only site that shows plots of total return on investment (besides mutual fund company websites, which only show performance for their own funds). Compare the data here for LMVTX with the data here for FLPSX. It gives FLPSX’s 10-year annualized return as 16.82% vs. 14.71% for LMVTX. That looks more like it! Over the same period in Yahoo, 1996-2006, we see a completely different picture (the incorrect picture).

On Morningstar it is not possible to compare two different funds on the same plot, so charting is useless in my opinion, except for comparing with the indexes and fund categories. The best solution is to look at figures like “n-Year Annualized Return” (see the Trailing Total returns section on Morningstar’s fund pages) at sites like Morningstar’s or on the mutual fund company’s pages themselves.

My apologies, as I have presented a few plots comparing mutual funds from Yahoo in the past. I guess this technically applies to ETFs and stocks as well, basically anything with distributions. I will try to go back and fix some of the old posts that used plots from Yahoo to compare past performance.

Thinking of Delaying that RRSP Deduction?

I’ve often heard the suggestion that if you are expecting to get a raise in the near future, make your RRSP contributions now, but wait until you are in that higher tax bracket to make that RRSP deduction. You’ll find this advice in many sources.

Is hoarding the generated deductions until you can make the most use of them, ie. when you are in the highest tax bracket a beneficial strategy? Let’s analyze the two cases:

  1. If I use the RRSP tax deduction now, I can take the tax refund I receive in April and invest it now, rather than later.
    Let’s say my marginal tax rate is T1. So making an RRSP deduction of R now will generate an RT1 tax credit in April. Let’s say that I am planning on getting a raise, or changing to a new, higher-paying career n years from now. Let’s assume I can reinvest my tax rebate and earn an annual rate of return of i. So in n years, my tax rebate will have grown to R(T1)(1+i)n.
  2. If I instead use the RRSP tax deduction later, when I am in a higher tax bracket of T2, I will get a larger tax refund, but I will have lost out on any earnings my money might have made in 1). My tax refund will be RT2.

So, it makes sense to take that RRSP deduction if T1(1+i)n > T2. It doesn’t look so complicated after all. Let’s plug in some numbers. Let’s say that you’re currently in a 31% tax bracket, and are expecting to move into the 38% tax bracket in the future. Let’s also assume that i=7%. Solving for n, we get n > 3. So if you are expecting a raise more than 3 years in the future, it makes sense to make that RRSP deduction now. And a smaller change from the 31% tax bracket to the 34% tax bracket yields n > 1.4. You can also fix your time n and solve for the new tax bracket T2.

Since raises are hard to predict with certainty, delaying RRSP deductions will most likely only make sense for people who are moving up several tax brackets (ie. those going to school earning summer/co-op income while making RRSP contributions and transitioning to full-time careers). Although even in this case, because it is not possible to predict the future, I would take the tax rebate now rather than later.

It is important to realize the difference between contributions and deductions. There is no reason why you shouldn’t make those contributions as soon as possible. I’ve heard people telling me before, to not put money into RRSPs until you are older and “until you have taxable income are able to make use of them.” This is utter nonsense and comes from the confusion between contributions and deductions. Most working adults make their contributions and deduct the full amount on their next tax return, so contributions, to them, are one and the same. But in general, they aren’t.

Make your contributions as early as you want (as soon as you have the room) so it can grow inside the RRSP without having to pay tax on any dividends or capital gains you might generate when you buy & sell. Use your deductions later on, as soon as you have taxable income, or later, if you plan on getting a raise (check to see if it’s worthwhile using the formula above).

Canada Student Loan vs. BMO Line of Credit

We have a BMO line of credit and a Canada Student Loan. The interest rate is prime (5.0%) on the former and prime + 2.5% on the latter (7.5%). You would think that it would make sense to put everything in the much cheaper line of credit, but this is the first year that we have started to pay down either, and I knew that we received a federal and provincial tax credit on interest payments for the more expensive prime + 2.5% student loan so I figured it probably worked out to be about even, and besides, our student loan is a lot smaller than the line of credit (although not significantly close to $0 yet to not worry about it). Without looking at the actual numbers, I had no idea. It’s one of things that no one can tell you the answer to (except maybe your accountant if you have one) and there is usually no universally true answer either. Anyways, I finally crunched the numbers and here’s what I got:

The annual interest owed in one year on the line of credit is Q(1+p), where Q is the amount drawn from the line of credit and p is the prime rate. The interest owned on the loan is Q(1+p+0.025), where Q is the amount owed of the student loan. But with the interest payment tax credit, the effective annual interest payment is reduced to Q(1+p+0.025) – Q(p+0.025)0.2105 = Q(1.0197+0.79p), where 21.05% is the tax credit rate, including the federal rate and provincial rate for BC.

So the loan is worse when Q(1.0197+0.79p) > Q(1+p). Re-arranging yields, p < 0.09 or "the loan is worse than the line of credit when p < 9%" Since the prime rate is currently at 5% at BMO, it looks like we are better off paying down the Canada Student Loan using funds from the line of credit. This will not only save us some money every year but will give us one less monthly payment to worry about and simplify our debt into one amortization plan. Simple is always better.

New Book: A Mathematician Plays the Stock Market

Just got a Christmas present from a very good friend of mine (same person who got me the Intelligent Investor for my birthday earlier this year) called “A Mathematician Plays the Stock Market” by John Allen Paulos. It appeals to me right away because of my math background and because I like to understand things like the stock market in quantitative ways. I’ll give you the blurb on the back:

With his trademark stories, vignettes, paradoxes, and puzzles, John Allen Paulos addresses every thinking reader’s curiosity about the market–Is it efficient? Is it rational? How should one pick stocks? Can one quantify risk? What are the most common scams? Is there a way to really outperform the major indexes? Can a deeper knowledge of mathematics help beat the odds? This wry and illuminating book is for armchair mathematicians, market followers, or anyone who wants to know how market work.

Some of the sections within the chapters that caught my eye were: “Technical Strategies and Blackjack,” “Efficiency and Random Walks,” “Fat People, Fat Stocks, and P/E,” “Are Stocks Less Risky Than Bonds,” “The St. Petersburg Paradox and Utility,” and “The Paradoxical EFficient Market Hypothesis.” There are many more topics. Practically everything in the investing world is touched on in some way. I am looking forward to reading it after I finish the book(s) I am reading now.