You've reached the internet home of Chris Sells, who has a long history as a contributing member of the Windows developer community. He enjoys long walks on the beach and various computer technologies.
Sunday, Jun 29, 2003, 12:00 AM in Money
The "Average Return" Myth
Let's say that you have $1000 to invest. The first year, you invest it and get a 25% return, so you leave your money invested. The next year, the market doesn't do as well and your return is -15%. What's the average rate of return over the two years? You way think that it's 5%, that is, (25% + (-15%))/2. Let's do the math for 25% and -15%:
- Using simple interest, after 1 year, $1000 + $1000 * 25% = $1250
- After 2 years, $1250 + $1250 * -15% = $1062.50
Here we're using Interest = Principle * Rate * Time calculation for yearly aka simple interest (I = PRT and Time is 1 year). Taking the numbers the other way, i.e. -15% the first year and 25% the next year, yields the same result:
- After 1 year, $1000 + $1000 * -15% = $850
- After 2 years, $850 + $850 * 25% = $1062.50
In fact, the result is the same no matter in which order that the rates come or how many there are:
Table 1: From Good to Bad
| year | return | total |
| 0 | 0 | $1,000.00 |
| 1 | 25% | $1,250.00 |
| 2 | 15% | $1,437.50 |
| 3 | 5% | $1,509.38 |
| 4 | -5% | $1,433.91 |
| 5 | -15% | $1,218.82 |
Table 2: Starting Bad to Good
| year | return | total |
| 0 | 0 | $1,000.00 |
| 1 | -15% | $ 850.00 |
| 2 | -5% | $ 807.50 |
| 3 | 5% | $ 847.88 |
| 4 | 15% | $ 975.06 |
| 5 | 25% | $1,218.82 |
Table 3: A Mixed Bag
| year | return | total |
| 0 | 0 | $1,000.00 |
| 1 | 25% | $1,250.00 |
| 2 | -15% | $1,062.50 |
| 3 | 5% | $1,115.63 |
| 4 | 15% | $1,282.97 |
| 5 | -5% | $1,218.82 |
This result surprised me. I found it unintuitive that no matter how the rates vary over time, it doesn't matter if they come first, last or in between. I expected large losses up front to swamp later gains or early gains to make up for late losses, but the change of the underlying principle amount evens things out, e.g. a smaller percentage drop later is against a larger principle if there have been early gains.
When you figure it as a single formula, Future Value = Principle * (1+Rate1) * (1+Rate2) * (1+Rate3) * (1+Rate4) * (1+Rate5) or F = P*(1+R1)*(1+R2)*(1+R3)*(1+R4)*(1+R5), the independence of the order makes more sense, since multiplication is commutative, i.e. it doesn't matter in what order you do it:
f = p* (1+r1)* (1+r2)* (1+r3)*(1+r4)* (1+r5) f = $1000*(1+25%)*(1+15%)*(1+5%)*(1-5%)* (1-15%) = $1218.82 f = $1000*(1-15%)*(1-5%)* (1+5%)*(1+15%)*(1+25%) = $1218.82 f = $1000*(1+25%)*(1-15%)*(1+5%)*(1+15%)*(1-5%) = $1218.82
Having varied rates like in Tables 1-3 in a stock or stock mutual fund investment isn't uncommon (as we've just seen during and after the Internet bubble). On the other hand, if you compare this a fixed yield (like a bond) with our "average rate of return" of 5%, you'll see a different result:
Table 4: Small But Fixed Rate of Return
| year | return | total |
| 0 | 0 | $1,000.00 |
| 1 | 5% | $1,050.00 |
| 2 | 5% | $1,102.50 |
| 3 | 5% | $1,157.63 |
| 4 | 5% | $1,215.51 |
| 5 | 5% | $1,276.28 |
With a fixed interest rate, we can simply our calculations somewhat using Future value = Principle * (1 + Rate)^Number of compounds. So, $1000 at 5% for 5 years is:
f = p*(1+r)^n f = $1000 * (1 + 5%)^5 f = $1000 * (1.05)^5 f = $1276.28
Any way you calculate it, not only does the boring, fixed interest rate bond out-perform the variable rate even for the same average rate of return, but clearly our average rate of return calculation isn't very useful. We're not really getting 5% year to year on our varied stock rates of return, or they'd show the same results as the bond. Instead, if you reverse the formula for Rate, we get:
r = (f/p)^(1/n) - 1 r = ($1218.82/$1000)^(1/5) -1 r = 1.21882^(1/5) -1 r = 4.037%
This gives us a annualized rate of return:
Table 5: Annualized Rate of Return
| year | return | total |
| 0 | 0 | $1,000.00 |
| 1 | 4.037% | $1,040.37 |
| 2 | 4.037% | $1,082.37 |
| 3 | 4.037% | $1,126.07 |
| 4 | 4.037% | $1,171.52 |
| 5 | 4.037% | $1,218.82 |
Taking this further, because the future value of an investment is the same whether you consider a fixed rate of return or a variable rate of return, for any principle, you can calculate the fixed rate of return by deriving from this formula (assuming r0 is the fixed rate of return and r1-r5 are the variable rates of return):
p*(1+r0)^n = p*(1+r1)*(1+r2)*(1+r3)*(1+r4)*(1+r5)
Further, because principle plays the same role on each side of the equation, you can remove it:
(1+r0)^n = (1+r1)*(1+r2)*(1+r3)*(1+r4)*(1+r5)
Solving for the annualized rate of return from the variable rates of return gives you this:
r0 = ((1+r1)*(1+r2)*(1+r3)*(1+r4)*(1+r5))^(1/n) - 1
Applying it in our example:
r0 = ((1+25%)*(1+15%)*(1+5%)*(1-5%)*(1-15%))^(1/5) - 1 r0 = (1.25*1.15*1.05*0.95*0.85)^(1/5) - 1 r0 = 4.037%
So what happens when we increase the variability, but leave the average rate of return the same? The variability adjusted return gets smaller:
Table 6: Extended Variability
| year | return | total |
| 0 | 0% | $1,000.00 |
| 1 | 25% | $1,250.00 |
| 2 | -15% | $1,062.50 |
| 3 | 5% | $1,115.63 |
| 4 | 15% | $1,282.97 |
| 5 | -5% | $1,218.82 |
| 6 | 5% | $1,279.76 |
| 7 | -25% | $ 959.82 |
| 8 | 40% | $1,343.75 |
| 9 | -30% | $ 940.62 |
| 10 | 35% | $1,269.84 |
Notice that we're still got an average rate of return of 5%, but increasing the variability gives us an annualized rate of return of 2.42%.
On the other hand, extending the same average without increasing the variability looks like this:
Table 7: Extended Time, Variability Unchanged
| year | return | total |
| 0 | 0% | $1,000.00 |
| 1 | 25% | $1,250.00 |
| 2 | -15% | $1,062.50 |
| 3 | 5% | $1,115.63 |
| 4 | 15% | $1,282.97 |
| 5 | -5% | $1,218.82 |
| 6 | 25% | $1,523.53 |
| 7 | -15% | $1,295.00 |
| 8 | 5% | $1,359.75 |
| 9 | 15% | $1,563.71 |
| 10 | -5% | $1,485.52 |
In this case, when the variability remains unchanged, the annualized rate of return remains unchanged at 4.037%. In other words, as the variability increases, the annualized rate of return gets further away and lower than the simple average rate. On the other hand, as the variability decreases, the annualized rate approaches the maximum value of a fixed rate of return, i.e. zero variability.
So, while it's comforting that so long as your investment doesn't go to zero, it doesn't matter when the highs and lows come, it's somewhat unintuitive that the average rate of return is not what you want to use to calculate the rate of return that you're actually getting. In fact, the annualized rate of return will always be lower than the average rate as variability increases.
Sunday, Jun 22, 2003, 12:00 AM in Money
"Them that know, don't tell"
In general, I suspect all members of the financial education market, from authors to radio talk show hosts and everyone in between. When I obtain financial independence, I don't plan on teaching anyone but my own friends and family. Why would anyone do otherwise except to fleece the public?
And then, having said that, I realize that every single book I've written, I wrote because I had a burning story to tell; I couldn't not write it. My motivation to write novels is grounded in my need to take my writing into a completely different direction w/o the requirement of generating an income stream. So it's likely that at least *some* of the folks in the financial education market are in it for love, but how can you tell which ones?
Further, it's not generally true that "them that know, don't tell." I know that I know how to write real software and how the technologies that form the topics of my writings and teachings really work, so at the very least, I'm the exception to that rule. However, there are an awful lot of exceptions, like all of my friends in the Windows developer education industry, so I reject the rule out of hand for at least a significant percentage of participants in any given field of education (certainly a significant percentage of them conform to the rule, of course, and those are likely to out number the ones that are the exception).
However, all of us in the Windows developer education industry make our living on education, not on the technology itself. We've chosen education because it's more lucrative then being a practitioner. (This may help explain why elementary school teachers choose their field: can you think of a place that they can make more money on basic readin', 'ritin' and 'rithmatic than as a teacher?)
So, if it's the case that education is more lucrative than practice, why should I buy someone's financial book, since they've obviously decided that selling me a book is more profitable than practicing what they're preaching. Further, the real-time markets have the built-in handicap that when a technique for really making money is widely put into use, the market adjusts for it, bringing the returns for that technique back in line with the market as a whole. If I discovered a new way to make real money, publishing how it works is the last thing that I want to do. Definitely, those kinds of books, like The Motley Fool's Investment Guide, are not what I want to put my trust into.
Things I find I can trust more are books that inspire me, like Rich Dad, Poor Dad, or change the way I look at things, like Fooled by Randomness, or help me to establish a foundation of knowledge, like Investing for Dummies or Learn to Earn. These are books that don't promise to make me rich (except the Rich Dad, Poor Dad books, but I've learned to discount that promise : ), but that help me align my brain cells so that I can take control of my own financial health.
So, all of this boils down to "Be a skeptic" from the Epilogue to Effective COM, furthering my belief that the ability to learn how one system works, e.g. COM, can be effectively translated into learning how another system works, e.g. investing. And so what's my motivation for this writing and others like it? It's purely selfish, I assure you. Writing something clarifies my thinking and posting it gets me access to, and feedback from, like-minded folks that can help clarify my thinking even more.
Sunday, Jun 22, 2003, 12:00 AM in Money
Chris's Notes on Cashflow Quadrant
Chris's Notes on Cashflow Quadrant: Rich Dad's Guide to Financial Freedom, Robert T. Kiyosaki and Sharon L. Lechter, Warner Books, April, 2000. I recommend this book for the way it twisted my head around.
There aren't any "how to" details in this book, but it still had some pretty valuable ideas in it that really changed my thinking and inspired me about what's possible:
- There are four main ways to make money: as an employee, being self-employed, running a business and investing.
- Our society has trained the middle and lower classes that success looks like getting a good job and being a good little consumer. I'd long recognized the cycle of get into college->get a good job->save for your kids' college education->they do it all over again for their kids, but I didn't know what alternative I had.
- The alternatives, according to this book, are running a business and/or investing. Specifically, this book really pushed running a business to fund investments, mostly for the tax benefits. My own thoughts are that having a business to fund investments is the absolute right thing to do. However, having a business that generates extra money to invest is easier said than done. If that's your plan, you should go away and do that first, then figure out the investing thing later in your leisure by the pool.
- Folks that run their own business or invest have a reasonable chance for financial independence, whereas employees and the self-employed do not.
- Financial independence has a specific definition: having more passive monthly income than your monthly expenses. Only when's it's passive income, i.e. you don't have to do the work to generate the income, do your finances allow you to pursue whatever activities you want, regardless of their income generating abilities, e.g. write a novel or home school your kids.
In general, I really like the way that Kiyosaki writes, although it's very marketing-style, so it turns me on and off at the same time. What I like is that he writes in a very personal way, talking about his two fathers, one trapped in the rat race like most of us and the other who'd learned how to become financially independent. He uses examples of his fathers' behavior to illustrate his points and talks a lot about how be changed his own thinking to break himself out of the cycle.
On the other hand, it seems like his major business is selling financial education-related materials to fuel his own wealth, so right away you have to suspect his motives. Also, his books are light on details, although he's happy to use them to point you at other produces that he or his partners have produced for more information. That's not a business model that respects the needs or intelligence of his audience. Still, if you ignore that and look for the ideas, I find his writing useful.
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