Category Archives: finance

Why do we use relative numbers for gains and losses?

I suppose you’re very familiar with hearing news like “The Dow is down 2.5% today,” or “The S&P is up 3%.” Mapping into basic mathematics, that would be -2.5% and +3%, relatively speaking.

But why are these figures couched in relative numbers? In my previous article about rebalancing my portfolio, I talked about a scenario where we suffered a -50% loss, followed by three +20% gains. Calculating the average annual gain was easy: +2.5%. But the ACTUAL gain was harder to figure out. Do you know why? Because everything we read and hear on the news is oriented towards calculating the arithmetic mean, which can give a real false positive on the situation.

I’m not alleging there is some huge controversy to cover up the real performance of the investment products. It’s more likely that the math to calculate the arithmetic mean is simpler and easier to understand than what we should be doing to properly evaluate something. What we SHOULD be using is the geometric mean.

  • Arithmetic mean is when we add up all four of numbers up above and divide by four.
  • Geometric mean is when we multiply all four numbers together and take the 4th root.

First of all, geometric mean doesn’t work with relative numbers. Can you imagine what -50%*20%*20%*20% ^ 1/4 would equal? If you studied advanced math, then you realize this would involve taking the square root of a negative number. Actually when something neither grows or declines, we multiply by 1. A 50% loss is represented as 0.5, or half of 1. A 20% gain is 1.2. You get the idea?

Our original scenario would be (0.5 * 1.2 * 1.2 * 1.2) ^ 1/4 = 0.964. Since this is below 1, it is a loss (as it should be!) This comes to roughly -3.6% annual loss (instead of the +2.5% we figured out earlier).

So there you have it: the way you calculate things can tell the difference between a loss or a gain. Now let’s check this out with a more realistic situation, like the performance of the S&P 500 index. That is something we always hear people citing.

The S&P showed the following average gains/losses (in %) from 2001-2010: -13, -23.4, 26.4, 9.0, 3.0, 13.6, 3.5, -38.5, 23.5, and 12.8.[1]

If we add up all 10 numbers and then divide by 10, we get => +1.69%. A paltry gain, but there were two market corrections, so not too bad, ehh? After all, the total gain (when we don’t divide by 10) was 16.9%, right?

Sorry, but that is wishful thinking. If we convert them to absolute numbers and then calculate the geometric mean by multiplying together and taking the 10th root, we get => 0.995, or a -0.5% loss. Total loss over that 10 year span (when we don’t take the 10th root) was really -4.7%.

Compared with our assumed total gains, this is more than a 20% gap! The differences between arithmetic and geometric mean can be devastating, especially if you were planning on retiring anywhere in the last decade.

The differences between what financial pundits say on TV shows and what is really happening can be huge!

Remember in that last post how I talked about an EIUL, or Equity Indexed Life Insurance policy, and how it could shield us from losses? Well, let’s run that scenarion and assume our money has been saved up in an EIUL. For this example, we’ll assume our EIUL has a minimum of 0% and maximum of 15%.

Revised numbers for 2001-2010: 0, 0, 15, 9, 3, 13.6, 3.5, 0, 15, and 12.8.

I know what you’re thinking. Doesn’t look good getting nipped on those really big gains, does it? Instead of the first 26.4%, we only get 15%. And trading in that 23.5% for 15%? Whew! But what is our REAL performance given all this? What if we calculate the geometric mean?

Result: 7.0% average annual growth. Wow! Compare that with our -0.5% loss. Total growth over 10 years was 96%. We almost doubled our money over that time span. Compared with basically standing still in the face of an average 2-4% inflation makes our EIUL a tremendous boon compared to some 500 index fund.

This begs the question: why do people use the arithmetic mean so much? For one thing, it’s easier. Your simple calculator is able to divide by 10, but you probably needed a scientific one to calculate the 10th root. It also may stem from certain financial calculations being valid with the arithmetic mean. For example, a financial instrument that is providing you with money without having it’s principle value being impacted. A key example here are dividends. If you hold a certain amount of stock and are taking cash dividends, then the capital value of your shares aren’t part of the equation. The dividend yield is what’s important. If you aren’t reinvesting the money, than simply averaging the numbers over a certain period of time will give you an average amount of dividend money you can expect to receive. But if you start investing the money back into the stock, your principle value will start to change, and this simple math tool is no longer valid.

So the next time you hear people give average rates of return on various products, think twice and double check how they are making their calculations. It can mean the world between gains and losses.

UPDATE: For the previous set of numbers, I used a spreadsheet, and found it clunky because there was no equivalent to SUM(list) like MULTIPLY(list). Instead, I wrote a short scala application. (Stay tuned for this getting published). After verifying the above numbers, I went on to add S&P 500 performance numbers all the way back to 1971. Here are the results:

Arithmetic mean of the S&P 500: 8.31%
Geometric mean of the S&P 500: 6.76%
Total growth factor: 13.7 x your original money

Arithmetic mean of our EIUL: 8.70%
Geometric mean of our EIUL: 8.50%
Total growth factor: 26.1 x your original money

A) If you hear people saying that the S&P performs close to 12%, well then, the last 40 years don’t reflect that. B) The differences when you remove losses is almost a 2% boost, which over 40 years can result in doubling your money.

[1] –

I am not a licensed financial advisor nor an insurance agent, and cannot give out financial advice. This is strictly wealth building opinion and should be treated as such.

Rebalancing my portfolio – Part 1

I’ve recently started a plan to rebalance my portfolio. The first leg is to stop investing in my 401k, and instead route that money into an overfunded Equity Indexed Life Insurance policy (EIUL). More on exactly what that is in a moment.

Mutual funds won’t earn you 12%

Over the past six months, I have done a LOT of reading and analysis. Did you know that over the past 20 years, investors have averaged no more than 4% return on investment when using mutual funds? Google for Dalbar report and see for yourself. To top it off, that doesn’t count taxes and inflation. Watch the video linked in here to see an example of a 401k that charges a whopping 3.6% in fees without the corporate 401k trustee even being aware of it. This is pretty bad, considering the person who originally crafted the ideas of 401k states that 1% fees should handles costs as well as provide a reasonable profit margin. With fees that high exacting year-after-year, you could lose anywhere from 40-60% of your earnings by the time you reach retirement. To add insult to injury, the trustee managing your corporate plan may only be relaying what the 401k provider is telling him, and not seriously looking after your needs. This is why only YOU can be in charge of your money, and it really is YOUR responsibility to understand everything about your retirement plans.

Tax deferred is planning to fail

Are you saving money in a 401k plan tax deferred? Did it sound good to not pay taxes today and let more of your money grow before cashing in when you retire. Guess what. When you defer taxes for 30 years it can take as little as 5 years in retirement to spend all those tax savings. And don’t expect to receive a thank-you letter from Uncle Sam. They designed it that way, so consider that works-as-designed. The truth is, it is usually better to pay taxes now and retire as tax free as possible. This takes out the risk of tax increases or bigger income as you approach retirement. If you are planning to retire in poverty and with lower taxes in the future (a big gamble), then tax deferred savings may be fine. But I prefer to call that planning to fail.

Losses will cost you more than the gains

There is something people don’t realize, and most financial advisors don’t seem to mention: losses will cost you more than your gains. For example, what if you had $100,000 in your mutual fund and had the following returns: -50% the first year, followed by three years of 20% gains. What would your average annual return be? -50% + 20% + 20% + 20% / 4 = 2.5%. So…you should have $102,500 after your years, right? Wrong. Let’s walk through this year-by-year, and find out what our REAL gain would be.

  1. After taking a big hit in the first year, your account will be worth only $50,000. That’s pretty bad.
  2. But what will a 20% gain get us the next year? Only $10,000 more, bringing us to $60,000.
  3. The third year will pull us up to $72,000.
  4. And finally at the end of the fourth year, we end up at $86,400.

So with a nice 2.5% average growth, we actually lost a total of 13.6%! That’s because when you lose money, it takes a lot more to gain it back. Let me say this again:

When you LOSE, it takes MORE to get back to where you started.

10% loss requires 11% gain, 20% loss requires 25% gain, and 50% loss requires 100% gain. Do you really expect to have three years of 20% gains like we saw up above? Has this type of gain happened for you yet? I think not. This is the sort of thing, combined with people on TV and the radio promising 12% returns as the norm, that causes a huge majority of investors to chase after the hottest funds, and in turn losing a lot more than they realize.

Tax free and no losses is worth more than you know

The key thing we seek is something that will provide you

  • tax free income
  • no losses during the negative years

Well, when it comes to tax free, the first thing you are probably thinking of is a Roth IRAs. That is because Wall Street has been marketing this stuff HEAVILY! Roth IRAs only let you save up to $5000 a year, and only if you don’t make too much money. After a certain point, you have made too much money and you can’t save a nickel that way. Throw in the fact that you can only withdraw the money after a certain age, and these are basically off the table as an effective savings tool.

Some companies have started offering Roth 401ks. They invest after tax money, but neither of the two companies I have worked for offered them until very recently, meaning there is little to put in there. But 401ks are still subject to the high fees, so I just wouldn’t go there.

(There are very particular cases where I would use a Roth IRA, but for today’s discussion, I don’t see them as a central place to save money for retirement.)

In the previous section, we discussed the importance of avoiding losses more than finding gains. What would our scenario have looked like if we could just skip the negatives? What if I found you a fund that instead of losing money in a negative year, we just took 0%? Let’s call it our “special piggy bank fund”. For giggles, we’ll even take take it on the chin and accept no more than 15% gain if the markets rise more than that. What do you think that will look like?

  1. In the first year, the stock market drops 50%, but our “piggy bank fund” doesn’t change, effectively growing/losing 0%. That means we still have our $100,000.
  2. For the second year, the market rises 20%, but we are limited to just 15% growth. This leaves us with $115,000.
  3. In the third year, the market rises another 20%, but again we only get 15%. This will move us up to $132,250.
  4. After the last year of our scenario, the market rises 20%, but we only net 15%. This leaves us with $152,087.50.
So, by taking no losses and only getting a maximum of 15%, we ended up with a little over $152,000, or a 52% increase in value. Compare that to the $86,000 we ended up with earlier. Which plan would you choose?
Looking high and low for a no tax, no loss fund
Just where can you find this type of investment? No losses? That is something your advisor is more likely to laugh at than give you a real. answer.

It turns out that our “piggy bank fund” is an overfunded cash value life insurance policy. By “overfunded,” I mean putting as much money in as IRS rules permit based on the policy’s face value. By “life insurance policy,” I mean an equity indexed universal life insurance policy that doesn’t actually put money in the stock market or buy index funds that have the risk of negative years, but instead sells index-based options. This means that in negative years, no one buys the options, and your money stays where it is, effectively a 0% growth. But in positive years, they sell options to grow at 15%, and when the growth is 20%, people buy the options to make profit through arbitrage, helping us along the way.

Is this overfunding too good to be true? Well, yes and no. The reason to overfund is to minimize the cost. Insurance companies make money on the premiums based on the face value of the policy. A $10,000 policy is much cheaper than a $300,000 one. But you can’t buy a $10,000 life insurance policy and then stuff $10 million into it. Before the 1980s, that is essentially what the rich were doing, and the IRS stepped in and put an end to that. The premiums and profits reaped by the insurance companies on such a small life insurance policy were almost non-existent, while the tax savings and guaranteed growth rates were huge and TAX FREE. The IRS doesn’t like tax free, so they put limits in place. But if you fund up to these limits you can still do quite nice. In my book, if the IRS doesn’t like it, then I DO!
“But this is life insurance! You only reap the rewards when you die!” I know this is what people usually think of with regards to insurance, but it’s incomplete. You are allowed take out loans against your policy. When you eventually die, the balance of your loans is deducted from the face value of the policy, leaving you with whatever you didn’t spend. And here is the ka-ching: the loans are considered TAX FREE money, and you actually DON’T have to pay them back!

“You should never mix life insurance and investments.” This sounds like a catch phrase with no basis in real facts. Go dig in deep and found out the differences between overfunded insurance and plain, simpleton insurance. There is a big difference. A big, tax free, no loss difference. Given all these facts, I say it’s just fine to mix the two together, because that is how this type of insurance was designed in the first place!

The bottom line
Imagine putting $500/month into an EIUL with no losses, EVER! As another factor, let’s increase our monthly savings by 4% each year to symbolize pay raises and increased cost of living. After 25 years, this would add up to around $250,000 of outlaid money, but could conservatively (8% average per year) accumulate over $1 million in savings. Now, instead of putting any more money away, you start taking out annual tax free loans. If we estimate withdrawing for the next 20 years, we may be able to get about $80,000/year. Added up, that would yield $1.6 million in tax free withdrawals.  Now go and visit your 401k and tell me what it’s going to take to save enough to withdraw $80,000/year TAX FREE. Do you remember your financial advisor mentioning never taking out more than 4% each year? To get $80,000, you would need $2 million. To handle a simple 25% income tax, it would be more like  2.6 million.
Not. Going. To. Happen.
So when I hear Dave Ramsey or Suze Orman move beyond helping people get out of the black hole of consumer debt, and start bad mouthing whole life insurance, saying to never mix investments and life insurance I just smile and instead take the advice of rich people in past generations. Most life insurance agents don’t know how to set up overfunded life insurance the proper way. Instead they seek to line their own pockets with profits, which has probably produced this backlash and  the “buy term and invest the difference” mantra. This is where YOU must lookout for YOU. An agent willing to set up an overfunded policy as mentioned above usually takes a 50-75% cut in total commissions. This makes such agents hard to find, but they are out there if you know where to look. Contact me if you want to know more.
To wrap up this first stage of Rebalancing my portfolio, I can sincerely say I’m putting my money where my mouth is. This is not a case of “tis for thee but not for me.” It is a cornerstone of my overall trajectory in saving money for retirement, but not the only part. Call me up in 20 years, and we’ll see how our financial plans are doing. I sure hope I don’t meet you as a door greeter at Walmart while my family is vacationing in Florida, seeking extra pay to make up for a lack of accumulated value and infinite trust in someone else to take responsibility for your retirement.UPDATE: Now cross posted at, my primary site for discussing wealth building opinion.I am not a licensed financial advisor nor an insurance agent, and cannot give out financial advice. This is strictly wealth building opinion and should be treated as such.