Momentum Trading An ETF Portfolio Via A Programmatic Allocation Model

In a prior article, we showed how a stop loss could be combined with a simple moving average (SMA) to achieve higher returns while also limiting drawdowns, as compared to a buy-and-hold strategy. A key concept of the first article was the idea of providing an "alternate" ETF to the ETF targeted for trading. This article expands on that idea to show how to use a larger collection of ETFs, again with a stop loss and SMA. The result is an overall performance that exceeded most (if not all) of the individual ETFs during the period, and with substantially less drawdown during the 2008 financial crisis.

(This does not represent the strategy employed by SimpleAllocation.com in our proprietary model. This is a greatly simplified model, lacking some key benefits and analysis. However it is educational, and useful for investors who chose to not use our model.)

In the prior article, we selected one ETF for trading, and showed how providing one conservative alternate generally created higher returns. For this article, we will instead start with a collection of 35 ETFs that represent a range of 25 different fund categories. These categories are quite diverse, and represent a broad selection of stock and bond funds. (A full symbol list is included at the bottom of the article.)

Trading Decisions
In this article, we will again use a moving average on normalized price slope, combined with a stop loss, to make all trading decisions. The stop loss used is a 10% tracking stop loss (tracking, split and dividend adjusted**). Trading decisions are made on a fixed period. On the last day of each period we check the moving average of the normalized price slope for all of the ETFs, select the 5 ETFs with the highest value, and invest 20% of the account in each of these 5 ETFs. When a stop loss is hit, no reinvestment takes place until the start of the next investment period.

We will present one case: a monthly trading period, combined with a 100 day SMA, applied to our list of 35 funds. (All trading decisions are made on the last trading day of each month; closing prices are used in calculating returns.)

The chart below shows the results, with data starting on 02-JAN-2002. (It should be noted some ETFs included in this analysis did not exist in 2002, but they were included as they became available.) The results for each individual ETF are show, as well as the results for our proposed strategy in bold red (labeled SmpAllc). In all cases, we have modeled the results for a hypothetical account starting with $100K.

Results - 100 Day SMA

Results discussion

First, it needs to be pointed out that several of the funds that appear to have outperformed the strategy from 2003-2007, did not have data prior to the mid-2003. Thus they started with the same initial balance of $100K, but after the funds which did exist earlier had already suffered losses during the end of the 2001-2003 bear market. The important takeaway is that, over the long run, the diversification and stop loss pay off. The result is an overall performance that exceeded most (if not all) of the individual ETFs during the period, and with substantially less drawdown during the 2008 financial crisis.

We think this is an important demonstration of how some simple rules eliminated the time consuming search for the best funds, and replaced that with an algorithmic approach that forced some amount of diversification, limited drawdowns, and had excellent return.

Current Allocation

The current allocations are shown below. We will be tracking the performance of this model in the following Google Drive document: https://docs.google.com/spreadsheet/ccc?key=0ApFbWGaISDcDdG92QkNhOUVDWHY2UmVuRXJjUU5nZ0E&usp=sharing

Security	Allocation	Category	Description
VWO	20%	Diversified Emerging Mkts	Vanguard FTSE Emerging Markets ETF (VWO)
VOE	20%	Mid-Cap Value	Vanguard Mid-Cap Value ETF (VOE)
IDV	20%	Foreign Large Value	iShares Dow Jones Intl Select Div Idx (IDV)
SCZ	20%	Foreign Small/Mid Blend	iShares MSCI EAFE Small Cap Index (SCZ)
EFA	20%	Foreign Large Blend	iShares MSCI EAFE Index (EFA)

Conclusion
We have shown how using a SMA, combined with a stop loss, can be an effective tool set to allow an investor to allocate from a selection of ETFs and generate an overall return better than most of the individual ETFs, while also lowering the volatility and drawdowns. Previously, we showed how an investor can trade individual ETFs using a similar strategy.

Between these two strategies, an investor can either trade individual ETFs that they believe are set to outperform, or use a more diversified approach and benefit from (automated) diversification and a stop loss. Even without the additional complexity of the SimpleAllocation.com proprietary model, these strategies are solid performers.

Thanks for reading!
Paul F. Dunn - Owner
Simple Allocation LLC and SimpleAllocation.com

Disclaimer - Simple Allocation LLC and SimpleAllocation.com do not advise the use of this strategy for anyone. Past performance of any trading strategy is not a predictor of future returns. Check with your financial and investment advisors prior to any trading.
* Disclosure - I am currently long SCZ and VOE.
** Tracking, split and dividend adjusted stop loss - "Tracking" means that the stop loss tracks upward movements, and applies to the highest price since purchasing the security. "Dividend adjusted" means that you adjust price changes for dividends. The "adjusted price" quoted on many websites is just that, dividend and split adjusted.

Full symbol list - AGG, BIL, BIV, BLV, BND, BSV, CFT, DBC, DIA, EFA, EMB, IDV, IEI, ITE, IWD, IWF, IWM, IWN, IWO, JNK, MGK, MGV, PCY, RSP, RWO, SCZ, SHY, SPY, TIP, VO, VOE, VOT, VWO, VYM, WIP

Where to find us

---

 

SimpleAllocation.blogspot.com    Blogs on investing.  

   

 

facebook.com/SimpleAllocation    Updates and information for site users.  

   

 

Simple Allocation    Updates and information for site users. All updates are public, you do not need to add us to a Circle.  

   

 

linkedin.com/company/simple-allocation-llc    Updates and information for site users.    

   

 

seekingalpha.com/author/simple-allocation    Blogs on investing.    

   

 

twitter.com/smpl_allocation    Notifications of recently hit stop losses*, and pertinent news.  

   

 

youtube.com/user/SimpleAllocation    Video blogs.  

   

*Please do not use our Tweets as a substitute for stop orders. The Tweets will be based on end-of-day data after market close; these are NOT real-time alerts. Further, delays in, or corrections to, end-of-day data or other technical problems could result in significant delays. Complete stop loss history is now available. 

Roth vs Traditional IRA, Which is Better?

This is a frequent question. The usual answer is "it depends on future income tax rates", which is true. But that doesn't really answer the question. How much do income tax rates need to change in order to make a significant difference? Do investment returns affect the decision? This article is going to give some specific examples to show how a Roth and traditional IRA compare with changing income tax rates and investment returns. We will also show how "equal" contributions are not actually equal.

All calculations for this article used our IRA calculator spreadsheet, available on the calculators page of our web site.

Summary

• A contribution to a Roth IRA costs you more than the same contribution to a traditional IRA, because the Roth contribution was paid after tax. Many calculators fail to take this into account, resulting in the Roth IRA looking much better than it should.
• If income tax rates do not change, there is no income advantage to either plan; both will provide the same net retirement income. This is independent of investment return. 
• Higher future income tax result in the Roth providing more net retirement income, lower future tax rates mean the traditional IRA provides more retirement income.
• Early withdraws of contributions from a Roth IRA do not incur a penalty. Early withdraws from a traditional IRA incur a 10% penalty, in addition to income tax. A Roth IRA could thus be used as secondary emergency savings account. 
• It is up to the reader understand the magnitude of income tax changes required to make the Roth favorable compared to the traditional IRA, to predict the future, and decide which IRA type is "better" for them.

What is "better"?
Since the goal of this article is to understand which type of IRA is "better", we will define "better". For the purposes of this article, we define "better" to mean:

• Given contributions that result in the same net income (see below), the IRA type (Roth or traditional) that provides for the longest retirement is the better plan.

"Equal" contributions
Prior to showing how income tax rates affect the Roth versus traditional IRA comparison, we need to make a point regarding contributions. We see a common error in many comparisons of Roth versus traditional IRAs regarding contributions. The error is that the comparisons start by assuming you make contribution of equal amounts to each type of plan. The problem is that a contribution to a Roth IRA costs you more than a contribution to a traditional IRA, because the Roth contribution is after income tax.

Example:
In this example, a person has $100K in gross income, pays 25% average income tax, and a marginal rate 5% higher (or 30%). Then $6K are contributed to either a traditional IRA, or a Roth IRA; the traditional IRA contribution is before taxes and the Roth IRA contribution is after taxes.

Because the traditional IRA contribution reduces gross income, less income taxes are paid. In this example, a Roth contribution of $6K is equivalent* to the combination of a $6K traditional IRA contribution AND a $1800 contribution to a taxable account. Alternatively, you could have contributed $8570 to the traditional IRA, had no taxable account contribution, and still had a net income of $69K. (As of the time of this writing, the maximum contribution is $5500, and an additional $1000 catch-up for qualified individuals. To contribute $8570 to a tax deferred plan would require a 401K plan. The purpose of this example was just to show the difference of pre and post tax contributions, independent of contribution limits.)

* By "equivalent" we mean that both examples result in the same net income after contributions to savings; but the contribution amounts are not the same due to tax treatment.

All calculations for this article assume Roth contributions are reduced by taxes. Said another way, both the Roth and traditional IRA have the same pre-tax contribution amount.

What if you make the maximum contribution regardless of plan type?

You should consider challenging our fundamental assumption regarding equal contributions. That assumption is correct for someone who is planning on contributing the traditional IRA equivalent of a maximum contribution OR LESS. But a maximum Roth contribution, as just pointed out, is more after-tax dollars than you can contribute to a traditional IRA. If you are going to make the maximum Roth contribution, and contribution limits stay the same for both types of plans, the Roth will have an advantage over the traditional IRA. Why? No capital gains are paid on Roth returns, but the traditional IRA alternative is a maximum contribution plus an additional amount in a taxable account. The capital gains in the taxable account reduce the total return relative to the Roth IRA.

Examples

The remainder of this article will give examples to show how income taxes affect the IRA types. From one example to the next, we will only change one assumption. All charts will be kept to the same scale. Common to every scenario:

• Equal contributions (see above) of $6K/year pre-tax are made prior to retirement. (That means $6K to a traditional IRA, and $4200 to the Roth for the initial income tax rates. As tax rates change, so do the Roth contributions, in order to keep net income constant.)
• Initial average income tax rate is 25%, with the marginal rate always 5% over the average income tax rate.
• Contributions accumulate for 30 years, then retirement starts.
• In retirement, $30K/year is withdrawn for income; income taxes are paid in the traditional IRA, but not the Roth. (That is, $30K + income taxes are removed from the traditional IRA each year.)
• Income tax is the average total income tax (federal and state); it is not the marginal tax rate.

Unchanging taxes

Now let's look at an actual example of how the balances of a Roth and traditional IRA increase, then decrease, over time. With no change in tax rates, the traditional IRA produces a slightly longer retirement. This is because all Roth contributions were taxed at the higher marginal rate. If the marginal rate is zero, the retirement duration is exactly equal. Also note that the traditional IRA appears to have a much higher balance, but that is only because the account balance is the gross balance (income taxes not paid). Thus for a given income, you have to withdraw more money from the traditional IRA each year, and the traditional IRA balance depletes faster.

Increasing taxes

Now let's assume that taxes immediately start increasing by 0.5%/year, to a maximum of 40%. Now the Roth has an advantage over the traditional IRA. The reason is that all of the traditional IRA income is now taxed at the maximum rate of 40%, while the Roth paid lower taxes as contributions accumulated.

Decreasing taxes

We show this example not because we think income taxes will decrease, but to be consistent and show the counter example to the above. This time we modeled income taxes as immediately starting to decrease 0.5%/year, to a minimum of 10%.

Other considerations

Remember this is a blog post designed to investigate how income tax changes and investment returns affected the Roth versus traditional IRA decision. There are other considerations, and you should always consult with your financial and tax advisors before making any decisions. But there is one aspect of the Roth IRA we want to make sure everyone is aware of.

• Withdraws from a traditional IRA are generally fully taxable, as well as incur a 10% early withdraw penalty. (There are some exceptions to the penalty.)
• Early withdraws from a Roth IRA do not incur any penalty on contributions, and the contributions are removed prior to any gains. (See IRS publication 590.) 

Thus one way to use a Roth IRA would be as a secondary "savings" account that, should emergency needs arise, you could take withdraws from without penalty. (Again, the penalty is only on early withdraws on investment returns, which are removed after contributions.) 

Conclusion
Many Roth versus traditional IRA comparisons mistakenly compare equal contributions to both account types. This error greatly exaggerates the benefits of a Roth IRA. It is possible to create scenarios that lead to either plan type appearing favorable over the other. It is up to the reader to predict the future, and decide which IRA type is "better" for them.


Thanks for reading!

Paul F. Dunn - Owner

Simple Allocation LLC - Simple investment allocation for the experienced investor
www.SimpleAllocation.com

ETF Trading Using a Stop Loss - Limit Drawdowns, Maximize Returns

At SimpleAllocation.com we recommend the use of a stop loss when trading our model. This is frequently a source of questions from our users, as stop losses are considered by many to actually limit returns, not enhance returns. This article describes a simple trading system* that uses a stop loss, and shows how properly used stop losses can limit drawdowns and enhance returns.

First, lets cover how NOT to use a stop loss. The problems we generally see are:

• Getting out of an open position too quickly; the stop loss is in the noise level of the security being traded.
• Slow to reinvest, or no actual strategy for when and how to reinvest.
• No strategy on what to do with cash while not invested.

Here is an example of a poorly executed stop loss strategy: trade SPY (SPDR S&P 500 ETF) using a 5% stop loss (tracking, split and dividend adjusted**), and on the last day of each quarter check the slope of the 250 day moving average and invest when the slope is positive and the account is in cash. (All examples assume an all-or-nothing strategy; the account is either 100% invested, or in cash.) 

(Green line - buy-and-hold results for SPY. Red line - return using the strategy described above. The same colors and scale will be used for all charts.) 

The stop loss did limit the drawdown, but also didn't generate much return during the market rallies.

Here is a better example of how to use a stop loss. Again trade SPY, but use a 10% stop loss (tracking, split and dividend adjusted**). On the last day of each quarter check the slope of the 100 day moving average and reinvest when the slope is positive and the account is in cash. (Note that this "better use" is slower to sell, and quicker to reinvest, compared to the "poor use" case above.)

(Green line - buy-and-hold results for SPY. Red line - return using the strategy described above.) 

We're on the right track. Again the drawdown was significantly limited as compared to a buy-and-hold strategy. (The drawdowns were about 25% for our "better strategy", and 56% for buy-and-hold of SPY.) The obvious problem is that we didn't do anything with the cash when we were not invested.

It's tempting to stop there; you've limited the drawdown during the financial crisis, and achieved an average annual return of about 5.4%, compared to an average annual return of about 4.2% for SPY. Wow! You beat the index and limited the drawdown. What could be better?

Well, how about doing something with the cash when not invested? For this next example, let's do just as above, with this exception: uninvested cash is put into SHY (iShares Barclays 1-3 Year Treasury Bond), and before buying, the slope of the 100 day moving average of SPY and SHY are compared and the purchase is made on the ETF with the higher slope.

(Green line - buy-and-hold results for SPY. Red line - return using the strategy described above. Blue line - SHY) 

ETF trading - stop loss limits drawdown

There are several interesting points to make about this final case.

• Average annual return is now 7.9%.
• The biggest drawdown was NOT the 2008 financial crisis, but a 10% stop hit in early 2010. 
• By providing one alternative to SPY, which was very conservative by choosing 1-3 year Treasuries, we increase the overall return substantially. 

There were several instances in this data set where the timing, by chance, worked very well in favor of this strategy with these securities. By that we mean that if the reinvestment decisions were moved by only a few days one way or the other, the results changed significantly; generally for the worse, though better than the prior strategy that did not provide an alternative to SPY. When tested across many combinations of funds, we believe that providing one conservative alternative to your target fund provides beneficial results.

To prove that, we also tested this final strategy using SHY in combination with each of the following ETFs: AGG, EEM, EFA, HYG, IJH, IVV, IWF, IWM, IWN, IYY, VOE, VTI, and VYM. In all but 2 of 14 cases, providing SHY as an alternative increased the average annual return.

It is important to note that in all of the examples above, the investor was assumed to make just 4 purchasing decisions each year, all evaluated on the last day of each quarter. (Selling decisions were made as required by the use of the stops. After hitting a stop, the account was modeled as being in cash.)

Summary

We believe that a stop loss can be an important tool to all investors. Keys to properly using a stop loss are:

• Having an appropriate stop value given the volatility of the securities you trade.
• Having a strategy for how and when to reinvest after hitting a stop.
• Providing at least one (conservative) alternative to the security you trade.

Thanks for reading!

Paul F. Dunn - Owner
Simple Allocation LLC - Simple investment allocation for the experienced investor
www.SimpleAllocation.com

* The trading strategy described in this article is a simple approach that anyone can implement using trading tools available on the internet. This does not represent the strategy employed by SimpleAllocation.com in our proprietary model.

** Tracking, split and dividend adjusted stop loss - "Tracking" means that the stop loss tracks upward movements, and applies to the highest price since purchasing the security. "Dividend adjusted" means that you adjust price changes for dividends. The "adjusted price" quoted on many websites is just that, dividend and split adjusted.

Where to find us

---

 

SimpleAllocation.blogspot.com    Blogs on investing. 

 

 

facebook.com/SimpleAllocation    Updates and information for site users. 

 

 

Simple Allocation    Updates and information for site users. All updates are public, you do not need to add us to a Circle. 

 

 

linkedin.com/company/simple-allocation-llc    Updates and information for site users.   

 

 

seekingalpha.com/author/simple-allocation    Blogs on investing.   

 

 

twitter.com/smpl_allocation    Notifications of recently hit stop losses*, and pertinent news. 

 

*Please do not use our Tweets as a substitute for stop orders. The Tweets will be based on end-of-day data after market close; these are NOT real-time alerts. Further, delays in, or corrections to, end-of-day data or other technical problems could result in significant delays. Complete stop loss history is now available. 

How does Simple Allocation compare to a buy-and-hold strategy?

At www.simpleallocation.com, we have created a rotating allocation model. The model picks the recent "best" performers from a specified portfolio for investment during the next month or quarter. (We have two time frames that we model; monthly and quarterly.) The model is a "rotating" model due to this nature of rotating-in the top performers, selected from a larger portfolio of securities. The model will only allocate to a maximum of 6 securities at any given time, and may allocate to as few as zero securities. This article is a review of performance of this model to a buy-and-hold strategy using a variety of allocations with the buy-and-hold portfolio.

A frequent source of confusion is that we publish "annualized gains" with our model output, while most people will refer to the average annual return generated by some other model or system. Please read this blog post (Volatility - why two strategies with the same average gains can have very different total return) to understand that annualized gain and average annual gain can be very different. Average annual gain "inflates" the actual gain compared to what most expect. It is not a real reflection of what an investor could expect to achieve after compounding. The result is that people often see our modeled annualized gain, and not realize how good the modeled returns really are. (Yes, we could fool you with average annual gain, but we'd rather be honest. To us that means if you compound your annual gain, you get the expected return; not the case with average annual gain.)

That said, lets move to comparing the Simple Allocation method to a more common buy-and-hold approach. (Link to Google document used for the modeling. Make a copy and try it yourself. )

For all comparisons we will use the Simple Allocation ETF Portfolio 001 (http://www.simpleallocation.com/allocation-plans/etf/etf-portfolio-001) compared to some other mix of ETFs using a buy-and-hold strategy.

Simple Allocation ETF Portfolio 001 versus Lazy Portfolio (60% stock, 20% bond, 20% real estate)

For this first comparison we will use the following portfolio: 

• 30% - iShares Dow Jones U.S. Index (IYY)
• 30% - iShares MSCI EAFE Index (EFA)
• 20% - iShares iBoxx $ Invest Grade Corp Bond (LQD)
• 20% - iShares Dow Jones US Real Estate (IYR) 

Clearly the Simple Allocation model, with ETF Portfolio 001, is the winner.

• The Simple Allocation plan has higher return; $3.02 for Simple Allocation compared to $2.07 for buy-and-hold (starting with a $1 balance)
• The Simple Allocation plan had about an 18% drawdown during the 2008 downturn, compared to over 50% for the buy-and-hold strategy.

But this buy-and-hold portfolio does have a large real estate exposure. So lets try another allocation more weighted to stocks.

Simple Allocation ETF Portfolio 001 versus Lazy Portfolio (60% stock, 40% bond)

For this comparison we will use the following portfolio: 

• 30% - iShares Dow Jones U.S. Index (IYY)
• 30% - iShares MSCI EAFE Index (EFA)
• 40% - iShares iBoxx $ Invest Grade Corp Bond (LQD)

Again, the Simple Allocation plan is better; more gain, less volatility.

Lets try more stock, this time adding in value stocks.

Simple Allocation ETF Portfolio 001 versus Lazy Portfolio (80% stock, 20% bond)

For this comparison we will use the following portfolio: 

• 30% - iShares Dow Jones U.S. Index (IYY)
• 30% - iShares MSCI EAFE Index (EFA)
• 20% - iShares Russell 1000 Value Index (IWD)
• 20% - iShares iBoxx $ Invest Grade Corp Bond (LQD)

Again, the Simple Allocation plan is better; more gain, less volatility.

We are going to stop there, as we think you get the point.

There is one major issue we do want to address prior to concluding. The ETF Portfolio 001 has 36 securities from which the model chooses on any given month. When we model the lazy portfolio, we only modeled a maximum of 4 different securities. Of course, the Simple Allocation plan is never allocated to more than 6 securities at one time, sometimes less, so the comparison is more valid than it may seem.

Also, the whole point of the Simple Allocation strategy is that if you had a list of 36 securities from which YOU had to chose each month, what would you do? You'd pick a simple portfolio of 3-5 securities and buy-and-hold.

If you'd like to suggest a different portfolio for comparison, contact us via private message from one of our social media sites.

Thanks for reading!

Paul F. Dunn - Owner
Simple Allocation LLC - Simple investment allocation for the experienced investor
www.SimpleAllocation.com

Where to find us

---

 

SimpleAllocation.blogspot.com    Blogs on investing. 

 

 

facebook.com/SimpleAllocation    Updates and information for site users. 

 

 

Simple Allocation    Updates and information for site users. All updates are public, you do not need to add us to a Circle. 

 

 

linkedin.com/company/simple-allocation-llc    Updates and information for site users.   

 

 

seekingalpha.com/author/simple-allocation    Blogs on investing.   

 

 

twitter.com/smpl_allocation    Notifications of recently hit stop losses*, and pertinent news. 

 

*Please do not use our Tweets as a substitute for stop orders. The Tweets will be based on end-of-day data after market close; these are NOT real-time alerts. Further, delays in, or corrections to, end-of-day data or other technical problems could result in significant delays. Complete stop loss history is now available. 

Volatility - why two investment strategies with the same average gains can have very different total return

On the SimpleAllocation.com website, we frequently mention "lower volatility" being a benefit of using our model. Most people have a sense that volatility is only important because it can cause them emotional stress to see their portfolio value drop; though they don't mind the upside volatility.

There is more to volatility though, than just the emotional roller coaster it can create. Volatility actually reduces return. We'll say it a different way - two investment strategies can have the same average gain, yet very different total return. 

How can this be? Here is a very simple example: If I have $1, and I make 10% each year for 3 years, then at the end of the 3 years I have $1.33. ($1 + $1 * 10% = $1.1,  $1.1 + $1.1 * 10% = $1.21, $1.21 + $1.21 * 10% = $1.33). Clearly the average gain was 10%/year.

Now lets say I have variable gain each year; 20% the first year, -5% the second year, and 15% the third year. That is still an average gain of 10%/year. But at the end of 3 years, I only have $1.31.($1 + $1 * 20% = $1.2,  $1.2 - $1.2 * 5% = $1.14, $1.14 + $1.14 * 15% = $1.31)

OK, so with constant 10% gain, I got $1.33 after 3 years, and with a more variable but still 10%/year average gain, I wound up with $1.31. That doesn't seem like too big of a deal. Well, each year these issues compound; the more time that passes, the bigger the difference will become. Also the more volatility, the bigger the differences become. 

The data below is a simulation of variable versus constant gain. (Link to the Google spreadsheet used to create the chart and data.) Notice that the constant gain model on the left has a 9.07% gain, each year, for 20 years, just as the variable gain model on the right has an average annual gain of 9.07%. Yet at the end of 20 years, the constant gain account has $5.67, yet the variable gain account balance is only $4.47. (Both accounts started with $1.00) In this case the volatility was 17.32%. (That is the standard deviation of the annual gains was 17.32%)

How does this compare to the "real" market volatility? SPY, an S&P500 index ETF, since 1994 has had:

• An average annual gain of 9.86%
• A volatility of 19.54%
• Resulting in a average annualized gain of only 7.99% ("Average annualized gain" is the equivalent "constant gain". Link to a Google spreadsheet for the calculations.)

Investing in the S&P500, you would only have achieved 81% of the gain you might have thought you would achieve by looking at the average annual gain.

The moral of the story is that just because two strategies have the same average annual gain, does not mean they will generate the same return. Lower volatility generally means better total return.

Epilogue
An even easier example is this: You have $1, you make 100% one year, lose 100% the next. You have $0, yet your average return was 0%.

The message here is that you should not use arithmetic average, but geometric average. This is well known by professionals, but often not known by individuals. Individuals often get confused, because if there is no volatility, the arithmetic and geometric averages are the same. This article was written with individuals in mind; not as a piece to suggest that professionals do not know who to properly compute average return.

To compute the return, solve this equation for compound_return: (compound_return)^time = (final_value / starting_value)
compound_return = 10^(log10(final_value / starting_value) / time)
Where "^" means: raise to the power of

I.E. you start with $1, end with $5, over an 8 year period.
compound_return = 10^(log10(5/1)/8) = 1.2228, or 22.28% annual return.

An alternative method:
compound_return = (final_value / starting_value) ^ (1/time)
Or, using the values above:
compound_return = (5/1)^(1/8) = 1.2228, or 22.8%

Check this by noting that 1.2228^8 = 5.


Thanks for reading!

Paul F. Dunn - Owner
Simple Allocation LLC - Simple investment allocation for the experienced investor
www.SimpleAllocation.com

Where to find us

---

 

SimpleAllocation.blogspot.com    Blogs on investing. 

 

 

facebook.com/SimpleAllocation    Updates and information for site users. 

 

 

Simple Allocation    Updates and information for site users. All updates are public, you do not need to add us to a Circle. 

 

 

linkedin.com/company/simple-allocation-llc    Updates and information for site users.   

 

 

seekingalpha.com/author/simple-allocation    Blogs on investing.   

 

 

twitter.com/smpl_allocation    Notifications of recently hit stop losses*, and pertinent news. 

 

*Please do not use our Tweets as a substitute for stop orders. The Tweets will be based on end-of-day data after market close; these are NOT real-time alerts. Further, delays in, or corrections to, end-of-day data or other technical problems could result in significant delays. Complete stop loss history is now available.