# IRR & Your Portfolio Returns…

So you are considering an investment in the stock of a publicly traded company and you plan to dollar-cost average into that investment over say the next five years with \$1,000 invested at the start of each year. Based on your analysis, you estimate that towards the end of that 5 year window, that aggregate \$5,000 invested in that stock would be worth say around \$8,000. Is that a good investment? You can’t say until you have a benchmark to compare that to. So what could you have done instead with that money? You could have invested in a diversified portfolio of stocks that has an expected rate of return of say 8% for each of those 5 years. So that is your opportunity cost because if you screw up with that stock investment, this 8% is what you could have earned instead based on the way this scenario is framed. So again, is this investment worth it? To answer that, you will have to calculate the NPV or the Net Present Value of the sum of all cash flows in and out of that investment and if that NPV is positive, that investment is worth it. Wait…what? NPV?

Okay, you make that first investment of \$1,000 to buy that stock. Where did that money come from? Probably from a linked bank account which will now show a deficit in that same amount and that deficit is represented by a negative number in the NPV calculation. The next cash deficit of \$1,000 will occur exactly a year later. But that \$1,000 invested a year later is not the same \$1,000 today. Why? Because there is an element of time between the two events. So what did you do with that \$1,000 in the meantime? Maybe you didn’t have access to that capital and hence had to wait a year to make that investment. But if you had that capital, you could have deployed that in another investment, say in that diversified portfolio of stocks earning 8%. Remember, that is your opportunity cost, oftentimes also referred to as the discount rate, a rate at which you have to discount a \$ in the future to make it equivalent to a \$ today. So that \$1,000 a year from now is only worth \$926 today. Along the same lines, \$1,000 two years from now is only worth \$857 in today’s dollars and so on. At the end of 5 years, you sell that stock and get back \$8,000 and because it is a cash flow back into your bank account, it is represented as a positive number in the NPV timeline as shown below.

The math…

Positive NPV equates to a superior investment. What makes the NPV positive? A return on investment greater than the discount rate. That NPV math is equationized above with i being the number of time periods, Ci is the cash flow infused (a negative value) or cash flow returned (a positive value) for each of those time periods and r is the discount rate. That time period measure could be in days, months, quarters or years.

Okay, NPV is positive and that’s good but what was the actual rate of return of that series of investments? Also called the IRR or the Internal Rate of Return, this measure is the actual discount rate for that investment and is calculated by zeroing out the NPV and extracting the value of r.

That r for this stock investment turns out to be 16% – double the rate of what a broad portfolio of stocks is expected to return so this investment in theory is worth considering. But your life of course is not that simple. There are many aspects of the risk-return trade-off that you have to consider before plunging your hard earned dollars into this investment because a single stock does not a portfolio make.

We report annualized portfolio returns in the financial plans you receive every once in a while and those returns assume a onetime lump-sum investment at the start of each period. And that oftentimes is sufficient because all that matters is how the portfolio that is customized for your circumstances has performed in the past. Whether you dollar cost average into that portfolio or not is irrelevant because you know that you are in a plan that has historical precedence with respect to the rate and range of returns you can expect in the future. But sometimes you want to know what your actual rate of return is taking into account the fact that you seldom invest all at once and instead trickle into your plan through bi-weekly or monthly systematic contributions. The earlier investments you make are exposed to more time in the market than the later ones and hence, each cash flow into your plan will have a different investment timeframe and the IRR mentioned above allows us to calculate the actual blended investment return of all those cash flows.

Back to a scenario which is more real this time…my daughter who is about 11 has a small portfolio that is invested on the extreme end of the systematic risk spectrum and considering the fact that she will have this money invested for another 50 to 60 years, that’s probably not a bad choice. So what does this portfolio look like? About 60% US Small Cap stocks, 10% US Small Cap Value stocks and 30% International Small Cap stocks. That’s it. Only smaller, potentially faster growing companies spread across the globe. And this portfolio based on the past is expected to be extremely volatile and she is fine with that. The plot below shows the best and worst case returns for this portfolio for 1, 3, 5, 10, 15 and 20-year timeframes based on the extracted asset-class performance data for the 1987-2015 time period.

Best & Worst Case Returns; 1987-2015

So there was a year where this portfolio dropped by 40% but then again, there was also a year in this timeframe where the portfolio grew by 40%. Similarly, there was a 3-year window where you started with \$100 in this portfolio and at the end of that period, you only had \$70 left. And you had to wait 3 years for that. But on the plus side, the best 3 years doubled your money.

What else stands out in this plot? That the longer you remain invested, the less of a likelihood that you lost money. You actually never lost money in this portfolio if your timeframe was 5 years or longer.

Now if you were to go back 1, 3, 5, 10, 15 and 20 years, this is what \$100 invested in my daughter’s portfolio would have turned into. For 1-year, she invested at the start of 2015, for 3-years, she invested at the start of 2013, for 5-years, she invested at the start of 2011 and so on.

What \$100 turned into…1996-2015

2015 was a bit of a downer year where that \$100 at the start of the year left you with only \$97 towards the end. But had you invested at the start of 2013 (for 3 years total), that same \$100 would have turned into \$147 which is equivalent to a 13.6% annualized return for each one of those three years as shown in the plot below. She of course was not around for 20 years but if she were, that \$100 in her portfolio would have turned into \$671 or a 10% annualized return for each of those years.

What else stands out in the plot above? The power of compounding returns. Try to visualize a line that touches the top of each bar and you get to see the exponential growth of your money the longer you are invested.

Annualized Portfolio Returns; 1996-2015

The relatively depressed returns for the 10 and 15 year timeframes in the plot above look anomalous but then they make sense. The 10-year timeframe includes the 2008 housing market crash and the 15-year timeframe includes both the housing market and the dot-com crash. Even then, this portfolio did just fine.

But she did not invest in one lump sum in any given year and instead trickled or dollar cost averaged into her portfolio starting about 4 years back. Her actual contributions are different but assuming that she contributed \$100 each month starting January 1, 2012 with her last contribution being on December 1, 2015, her ending portfolio balance would have been \$5,809 based on what her portfolio has done. So she did 4 years x 12 contributions of \$100 each year or \$4,800 total and she only has a grand more to show for it? The reason why that difference is small is because she did not contribute all \$4,800 at once but trickled her way in. Some of those \$100 earned gigantic returns while others didn’t do as well. So what was her actual return or the IRR?

The math first…

The actual portfolio return hence is 9.5% annualized. That’s not very obvious to many investors thinking that they contributed \$4,800 to this portfolio and in the end, only have \$5,809 to show for it. And that too over four long years!!! But what we fail to account for is how and when that money was contributed. And this is precisely the stage where we start questioning our investment strategy which then leads us to ultimately abandon a fully-functioning plan. That to us is a tragedy because had you kept at it for a few decades and hopefully with more savings, you would be set. And that is the goal.

So the next time you see that portfolio of yours not budging at all, don’t fret. Your portfolio is growing but it’s just that the new funds flowing into your account mask the return on investment of the older contributions and that is all this very dull and dry write-up is trying to point out.

And as always, stick to your plan and remain invested.

Happy Investing.

Image credit – Andrea Allen, Flickr