A Dividend Growth portfolio is well suited to be viewed as a mini-index fund since it’s an allocation to a specific set of dividend growth stocks held with a long-term buy and hold strategy in mind. Here’s how you can make your own index fund from your stock portfolio.
But before we begin, the inspiration and credit for this post goes to The Investor’s article on How to unitize your portfolio at the Monevator blog. And a special mention also to Weenie from Quietly Saving who led me to it in one of her articles.
Danger, Math Ahead!
There’s some math involved in the introduction part of this article. The following link skips the theory and gets to the practical part.
The main focus on a DGI portfolio is the dividend income itself, and calculating portfolio performance via total return is of less importance. But some bloggers like to report their portfolio value and sometimes the growth.
Now supposing your stocks at the start of the month are worth $10,000 and at the end of the month they’re worth $12,800. This is an increase of 28% (12800 / 10000). But growth really means the increase (or decrease) that the investments did all by themselves. Perhaps you purchased more stocks in the middle of the month; perhaps stocks were sold – what would the growth be then?
In my monthly summary posts I use a simple formula to calculate growth on a month-to-month basis:
Growth = (Month End – New Capital) / Month Start
So using the starting / ending figures above and a new purchase of $1500 of shares I would get
Growth = (12800 – 1500) / 10000 = 13%
The ‘New Capital’ amount may be positive or negative depending on the amount of shares bought or sold. This formula simply removes any new capital from the final portfolio value and so it approximates what the end result might have been had those purchases not been made.
This is just an approximation and a more accurate method would take into account the date on which any purchases or sales were made. Consider what actually happens in the real-world using the example above.
The starting amount was $10,000 but because we’re in the real-world now, we need a date. Let’s go with 01-Jan-16. So on 01-Jan-16 we own $10,000 of a collection of stocks; it doesn’t matter which ones or how many since we’re looking at the portfolio as a whole. Starting from the beginning of January, the market will move however it does and the value of that $10,000 will change daily. This is the typical “growth of $10,000” chart that is commonly used to contrast investments.
On the 20th January, the night before making the $1,500 purchase, we look at our brokerage account and see that the current market value is $10,500. $10,000 turned into $10,500; a 5% increase. That’s great so we buy $1,500 more!
It’s unlikely that the new purchase will continue with that same 5% growth rate; nor is it likely that the $10,500 will grow another 5%. By making the $1,500 purchase our total return is now affected by a second growth rate as well as the historical growth from the start of the month until the purchase date.
Fast forward to the end of the month where we look at our statement again and see $12,800 as the end of month balance. We notice that the $1,500 purchase ended up being worth $1,600 and that the $10,000 ended up being $11,200. $11,200 + $1,600 = $12,800 and we’re happy!
The $10,000 starting amount yielded $11,200 or 11.2% while the $1,500 had a 6.67% growth. These values can be averaged and combined in a number of ways to produce a “total growth” percentage; two common methods are Money-Weighted and Time-Weighted. Both methods provide different results yet both are correct in their own way.
I’m just going to mention this briefly and then move along. With this method, the inflow and outflow of cash and their timing influences the weighting and final value. This is a common method for stock portfolio rate of return calculations. It’s a single rate of return value that can be applied to each transaction weighted by quantity and date which produces the final amount.
To calculate it, you use the XIRR function in Excel which given the values above, results in 314.8%. This is an annualized result however, to get the monthly result you must reduce the rate by the duration, in this case 31/365 days. The final result becomes
Monthly rate = (1 + 3.148)^(31/365) => 12.843%
This method makes my brain-cell hurt, so I’m going to copy what fund managers do to report their fund’s performance instead and that’s using a Time-Weighted method.
The Time-weighted method weights the investment performance equally by time and it doesn’t care about relative amounts of money because it uses the geometric total of the investment growth. In the example we worked through earlier we saw:
$10,000 -> $10,500 -> $11,200
$1,500 -> $1,600
The numbers in the example relate to a 5% growth from 1st Jan to 20th January followed by a 6.67% growth from 21st January to 31st January; for example $1600 / $1500 = 11200 / 10500 = 1.0667 (6.67%).
So in this case the time-weighted result = (1+0.05) x (1+0.067%) = 12%.
I mentioned this is how professional fund managers calculate their returns. The benefit of this method is that the results can be compared to other fund returns since the mutual fund industry is required to use them. So let’s put the theory into practice and make our very own index fund!
Making an index fund
I’m going to use real numbers from my Income Fund starting from 1st January this year. My Income Fund consists of stocks, stock funds, cash and bond funds; they’re all going to get combined into my index as I’m looking at my Income fund as a whole.
Step 1: Starting value
The first thing to do is look up the starting fund net asset value. This is the total market value of the assets in the fund. For mine it’s simply the market value as of 31 December 2015 which is also the starting market value on the 1st January 2016, and it’s $215,011.28.
Step 2: Choose a unit value for your new fund shares
Next you just need to pick the starting value of your virtual fund shares. This is entirely arbitrary; the higher the value the fewer shares you start with. I’m going with $100 per share and we’ll call this share value the “Unit Value” going forward.
1st January: Unit Value = $100
Step 3: Calculate your starting number of fund Units
The starting number of fund Units is the Net Asset Value dividend by the Unit Value. So that’s equal to
Number of Units = 215011.28 / 100 = 2,150.1128 Units
Rule #1: Number of Units x Unit Value = Net Asset Value
At any time, the number of units multiplied by the unit value is equal to the market value of the fund assets. We’ve only just declared the shares but a quick sanity check shows
Fund Assets = 2,150.1128 shares x $100 = $215011.28
Rule #2: Changes in Fund Asset values changes the Unit Value
As the market prices of your Fund Assets change, the number of Units in your Fund never changes; only the Unit Value does.
Unit Value = Fund Asset Value / Number of Fund Units
Rule #3: The number of Units only changes when you buy or sell Fund Assets
The main thing to keep track of is external money added or removed from the Fund Assets. Each time external money is involved you must buy or sell Fund Units. Here’s a worked example from the 4th January when I removed $90.77 cash from my Fund Assets and also bought $250 of VHDYX on the same day.
January 3rd was a Sunday, so the Unit Value of my fund was still $100, and I had 2150.118 Units. To transfer the $90.77 from my money-market account (included in the Fund Assets) to my checking account, I had to ‘sell’ $90.77 worth of Fund Units at $100 which resulted in -0.9077 units.
Yet I also bought $250 of VHDYX as an automatic transaction from my checking account. Since this money came from an external (checking) account and not from a money market account; I must ‘buy’ more Fund Units at the same $100 price, so I added 2.5 units.
Together these transactions meant a net inflow of +1.5923 Fund Units (and an increase in Fund Assets of 250 – 90.77 = $159.23). So on the 4th January I had 2150.118 + 1.5923 = 2151.7051 Units.
Now when the markets closed, I then needed to re-calculate the Unit Value because the Fund Assets prices had changed. At the end of the 4th January, the total market value was $212,196.83 thanks to a very poor start to the year in the market.
4th January: Unit Value = $212196.83 / 2151.7051 = $98.618
That’s a 100 – 98.618 = 1.382% drop on the first day of virtual trading! Total net assets decreased by 1.31% since although the Unit Value dropped, I now have more Fund Units.
The good news now is that I simply need to look at the Unit Value to see my Income Fund performance on any given day.
Handling of dividends
If you re-invest dividends (or interest) you don’t need to do anything with Fund Units; the re-invested dividends will increase the market value of your Fund Assets and hence increase your Unit Value.
However, if you withdraw dividends (or interest), you must sell Fund Units. This is because dividends are considered part of the Total Return of the investment. I found this an interesting point since it reinforces the point that withdrawing dividends is withdrawing capital.
In my particular investment scheme, all dividends are paid monthly into my money market account and then I transfer the total monthly dividend amount in one go to my checking account where it gets re-invested with automatic payments the next month. Since this counts as an external transfer I sell Fund Units for the monthly transaction; however dividends being paid into my money market account are ignored since the money market account is part of my Fund Assets.
In the same way, if I was to purchase new shares with money from my money market account that also wouldn’t require buying new Fund Units; that’s simply a reallocation of assets from one asset type to another and it’s all contained within the Fund Assets. But adding money to my money market account from my checking account is an external transfer and would trigger a Fund Unit purchase.
January results to date
I ran through the remaining transactions in my Income Fund up until 23rd January and the results are shown below. I use two tables in an Excel file; one a table of transactions and the other is the master Fund Asset list.
|Date||Type||Amount||Unit Price||# Units|
I have a lot of automatic transactions that dollar cost average into Fund Assets plus I’ve been buying more on account of the market drop this month; the withdrawals are dividend transfers as I mentioned above.
The master asset table looks like this
|# Units||Total Value||+/- Units||Total Units||Unit Price ($)|
I got a bit carried away calculating daily values. In reality you only need to calculate a day’s values when you buy or sell Fund Assets or at the end of the month if you want a monthly performance summary.
Original example re-worked
Edit: 24-Jan-16. Showing the 12% increase calculated from the example using the unitization method
Here’s the original example of $10,000 growing to $12,800 with a purchase of $1,500 done using the unitization method.
|Date||Total Value||+/- Units||Total Units||Unit Price ($)|
You can see that the final Unit Value is $112; an increase of 12% from the starting $100 value. This matches the 12% gain on investment from the earlier Time-Weighted calculation. We also gained 14.29 units as a result of the purchase, the only additional assumption for simplicity being that the market value didn’t independently change on the 21st except for the new capital added (i.e. the Total Value of the 21st was the Total Value of the 20th plus $1,500).
My Income Fund is down 100 – 96.202 = 3.698 % so far this year, we’ll see how it ends up at the end of the month as I’ll be using the Unit Value as one of my monthly metrics going forward.
Incidentally using my old approximation formula would have given a decrease of 3.711% so it’s pretty close. But it’s more fun to have my very own share price that I can follow.
In this post I found three different growth values for the same example: 13% with a simple approximation; 12.843% via Money-Weighted returns and 12% via a Time-Weighted return. When making any comparison of growth, it’s important to know the calculation method and timeframe that the growth values correspond to.
Quote of the day
Life is really simple, but we insist on making it complicated.