This week’s article is inspired by a question that came up during the Bicameral Working Group on the PFD hearing a few days ago. It centers on a portion of the PFD calculation. Here’s the gist:

Under the current law, the sum of the earnings over the last five years is multiplied by 21% in order to establish the amount of money available for distribution. One half of that number is what traditionally goes toward our PFD (minus a few technical adjustments). When that was explained, a member asked a question to the effect of “What’s up with that 21%?”

### Welcome Back

Before I get started, I should clarify something. Some of you may be aware that back in December, I agreed to help the new administration get situated. As a result, I put this website on hold to avoid any perception that this work was representative of the Governor’s position.

For the past half year, I’ve missed writing for you. But, now that my work with the administration is wrapping up, I’m back in action and ready to shed some light on a few of the issues that I follow.

As you may know, I like to write about things impacting Alaska’s economy that strike me as interesting, misunderstood, or generally lacking in the public domain. But, this isn’t a personal journal or a political propaganda tool. Nor is it a gossip column or news outlet. This website is simply my outlet for providing information to the public (should they care to read it). I always strive for these articles to be data driven, non-partisan, and apolitical.

So, thanks for reading and I hope it’s worth your time (and my effort). I’m going to ease back into this blogging thing with a short article today.

### Where did the 21% number come from?

What we know is that the 21% number came into being with a statute change in 1986. In the original language (from 1980) the calculation called for a simple average of the previous five-year earnings. But, with the passage of §1 ch 28 SLA 1986, that law was changed to be 21% of the sum of the previous five-year earnings.

While I haven’t reviewed the minutes from the bill that established that 21% number, I can do the math. And, while I can’t say for certain if this is what is in the legislative record, I will assume it is what drove the decision.

Before I try to explain what is happening, let’s look at the numbers. Take a quick look at what happens when you distribute half the earnings using the simple five-year average (I’ll just use a $100,000 starting balance and a 3.5% earnings rate for demonstration purposes):

#### 5-Year Average Earnings

Beginning Balance | Earnings | Distributions | Ending Balance | % Earnings Distributed |

$100,000 | $3,500 | $1,750 | $101,750 | 50% |

$101,750 | $3,561 | $1,750 | $103,561 | 49% |

$103,561 | $3,625 | $1,765 | $105,421 | 49% |

$105,421 | $3,690 | $1,781 | $107,329 | 48% |

$107,329 | $3,757 | $1,797 | $109,289 | 48% |

$109,289 | $3,825 | $1,813 | $111,301 | 47% |

$111,301 | $3,896 | $1,846 | $113,351 | 47% |

$113,351 | $3,967 | $1,879 | $115,439 | 47% |

$115,439 | $4,040 | $1,913 | $117,566 | 47% |

$117,566 | $4,115 | $1,948 | $119,732 | 47% |

And here is what happens when you use 21% of the five-year sum, rather than the simple average:

#### 21% of 5-year Total Earnings

Beginning Balance | Earnings | Distributions | Ending Balance | % Earnings Distributed |

$100,000 | $3,500 | $368 | $103,133 | 11% |

$103,133 | $3,610 | $368 | $106,375 | 10% |

$106,375 | $3,723 | $747 | $109,351 | 20% |

$109,351 | $3,827 | $1,137 | $112,041 | 30% |

$112,041 | $3,921 | $1,539 | $114,423 | 39% |

$114,423 | $4,005 | $1,951 | $116,477 | 49% |

$116,477 | $4,077 | $2,004 | $118,550 | 49% |

$118,550 | $4,149 | $2,053 | $120,646 | 49% |

$120,646 | $4,223 | $2,098 | $122,771 | 50% |

$122,771 | $4,297 | $2,139 | $124,928 | 50% |

## Results

Because of the averaging mechanism, and because of the retention of half of the earnings, the distribution amount converges at 47% of the current year earnings. This happens any time you use a moving average on a string of growing numbers – the average will always be lower than the most recent value. And so, multiplying a target rate by an averaged based will always underperform.

My guess is that there was someone like me around in 1986. And, that person probably pointed out the fact that if the intent was to distribute half the earnings, they would fall short under the law passed in 1980. The averaging method works to smooth out volatility, but it doesn’t fully capture the effects of compounding interest on the retained earnings.

Under the assumptions I used above, increasing the multiplier to 21% does in fact get you to 50% of current year earnings (once you have enough data). So, there you go.

### Side Note

There’s nothing particularly special about 21%. That number would be slightly different if you use a different return assumption or have different factors that influence the rate of growth of the fund. In fact, that 21% number turns out to have been a little low given the actual results of the fund.

As the legislature debates changing the growth rate of the fund, and the amount of deposits that now flow into it diminish, that 21% could be a little high looking forward. But, it serves its purpose.

Just remember – if the fund is growing, any averaging technique always produces smaller numbers than applying the same rate to the most recent year. This is true with the PFD formula, the new POMV formula, and any other formula that seeks to smooth out volatility. So, if you’re going to use averaging, you need to be aware of this fact.

### Another Important Issue

Using the 5-year average of earnings essentially means that the earnings from each year are distributed in five easy payments. So, if the earnings are $1,000,000,000 this year, and we only distribute half of the earnings, then we get $100,000,000 per year in each of the next five years. The next year’s earnings will layer on top of that, so each year we are actually getting a portion of each of the last 5-year’s earnings.

This means that $400,000,000 of the current year earnings stays in the bank, and will earn interest while it’s held for future distribution.

#### The Holding Account

This brings up another important tangent. The money in the fund is not all part of the money that must be protected to generate future earnings. At least part of that money already belongs to the beneficiaries, but has not become ready to distribute yet due to this smoothing factor.

This is why we have a second account within the Permanent Fund. It was formerly called the “undistributed income” account, which was a much more appropriate name for this purpose. It is meant to hold the undistributed earnings for future payments.

But, that account now holds more than the undistributed income. It also hold earnings that were not previously transferred to their proper accounts. It holds some money that should be in the principal account under inflation proofing rules, some money that should have went to the dividend fund in previous years, and some excess earnings that should have been transferred at the discretion of the legislature. Plus, all this extra money earns interest while it sits in the wrong account, which complicates the issue.

Anyways, we now know this second account as the “earnings reserve” account, or ERA. And, a lot of the confusion that exists today is a result of expanding the use of that account. But that is a topic for another day.

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