6. Passive Agressive

The concept of passive management is counterintuitive to many investors. The rationale behind indexing stems from five concepts of financial economics:

• In the long term, the average investor will have an average before-costs performance equal to the market average. After-costs, the average passive investor will still track the index; the average investor in actively-managed funds will have below-market returns, on average. Like Boggle likes to say, this is arithmetic - you can't argue with it!
• The efficient-market hypothesis, which postulates that equilibrium market prices fully reflect all available information, or to the extent there is some information not reflected, there is nothing that can be done to exploit that fact. To put it another way, in order to pick a "winner stock", it's not enough to pick up a winning company: you need to find a company who's going to success more than the market expects it to succeed. 
• The principal-agent problem: an investor (the principal) who allocates money to a portfolio manager (the agent) must properly give incentives to the manager to run the portfolio in accordance with the investor's risk/return appetite, and must monitor the manager's performance. The way mutual funds are managed today, there's little incentive for long-term performance. If the fund fails, the company will just close it and open a new one. It's always more fun to play with other people's money, but in this case the money is ours. 
• The local elasticity of the market makes stable strategies (such as indexing) more favorable. 
• The capital asset pricing model (CAPM) and related portfolio separation theorems, which imply that, in equilibrium, all investors will hold a mixture of the market portfolio and a riskless asset. That is, under suitable conditions, a fund indexed to "the market" is the only fund investors need.

This is all high talk, and I'll freely admit I don't understand all of it. But at the end of the day, the main reason index funds makes sense to investors is because they beat the majority of actively managed accounts. Consider for instance this research from the Vanguard group:

• Over 10 years, the S&P index has beaten more than three-quarters of all actively-managed funds
• Over 20 years, the S&P index has beaten more than 80% of all actively-managed funds
• Read it again: Over 20 years, the S&P index has beaten more than 80% of all actively-managed funds!

It turns out that the most aggressive investor is the one who sits and does nothing. Who would have known?

Next week, on why Indexing is bad for the economy. 

5. How Much Is Enough?

True story, Word of Honor:
Joseph Heller, an important and funny writer
now dead,
and I were at a party given by a billionaire
on Shelter Island.
I said, "Joe, how does it make you feel
to know that our host only yesterday 
may have made more money
than your novel 'Catch-22'
has earned in its entire history?"
And Joe said, "I've got something he can never have."
And I said, "What on earth could that be, Joe?"
And Joe said, "The knowledge that I've got enough."
Not bad! Rest in peace!"


--Kurt Vonnegut

John Bogle opens his 2009 book, Enough: True Measures of Money, Business and Life, with this story - published a poem in The New Yorker (May, 2005.) The book is a fun read, and although it covers a lot of the same areas as previous books (in particular Common Sense Investing), it's more personal this time.

The book also made me wonder how much is enough for me. My sister, who lives in Goa with her daughter, is happily retired with savings that allow her to spend about $10-15K a year. For myself, I'm budgeting $90K a year for retirement. Do I really need it? I know of people who plan to retire once they can guarantee an annual income of $150K. Are they crazy or am I not saving enough? What is enough and what is excessive?

Many factors go into my retirement planning, and the unknowns are greater than the knowns. To figure out my expected expenses, I started out with my 2010 spendings. It was easy to sum them all up from my bank account online statements (and using some nifty Excel tricks.) I removed all the deposits, of course, as well as expenses I don't expect to have in retirement (such as mortgage and toll payments.) The final number was surprisingly small: about $42,200. How did it balloon to more than double this number?

• Medical expenses: today I'm insured through my employer. Although Massachusetts (and soon, the rest of the US) enjoys universal insurance benefits, the minimal cost is still about $500 a month. Assuming I want the best coverage and allowing for emergencies and out of pocket expenses, I budgeted $1000 a month, or $12,000 annually.
• Travel: when I'm retired, I want to travel a lot. Add $10,000.
• Computer, cellphone (currently covered by my workplace): $1000 annually
• Car: I finished paying for my car, but I should assume $500 monthly for car payments and another $2000 for insurance (currently deducted from my paychecks): add $8,000 annually
• Property tax (currently paid through the mortgage company): $2,000 annually

The total came up to $75,200. I also assume an average tax level of 20% at retirement (including capital gain taxes, income taxes and state taxes). Taking this into account, I'll need to withdraw about $94,000 annually! Suddenly, much more than my earlier modest $42,200 calculation. 

This was surprising - I didn't expect it to be that high. More conservative assumptions can push it even higher: higher taxes, expensive hobbies, kids (if I decide to have them), unexpected emergencies. 

On the other side, I'm also not taking into account other sources of income, mainly Social Security and sharing expenses with my partner. For the former, with all the talks about Social Security eventual insolvency, I don't want to see it as more than a bonus payment of about $20,000 annually in 20-25 years. This is not going to make a big dent in my income in any case. I do have a partner that shares the expenses, but when it comes to my finances, I want to be independent. 

And then there's the question of inheritance. Here's the yuck factor means that I'm not going to assume anything, because taking it into account is too painful. 

This calculation cannot be made completely accurate. For example, when I'm 85, perhaps I won't travel as much and my hobbies/travel expenses will be lower. On the other hand, my medical expenses might be higher. I decided not to start nit-picking at each expense and assume that on average the total annual budget will remain the same. 

My bottom line is therefore $94,000 pre-tax. 

Running this number through the Safe Withdrawal Rate calculator resulted in my retirement goal: about $3.2M for my age, time horizon and my growth/inflation assumptions. Of course, I'm not there now, but it's fun to make the calculation and try to predict when I'll have enough. 

For me, "enough" is now well defined. RIP, Joseph Heller!

4. Math break: Safe Withdrawal Rate

This weekly blog is a little early, as I'm packing for a vacation in St John. The snow will have to wait until my return!

In my last blog, I talked about the formula that connects the expected rate of return, inflation, time period and SWR - the Safe Withdrawal Rate. To recap, the SWR reflects the annual amount you can withdraw from your account (adjusted to inflation) without running out of funds.

In this blog I'll show you how I derived the formula.

Let's recall the variables in the picture:

• N is the time period, in years
• G is the expected annual growth factor (for example, if you expect 8% average growth, G = 1.08)
• F is the inflation factor (for example, a 3% inflation corresponds to F = 1.03)
• R is the net growth, R = G/F

Our goal is to show that SWR is (1 - 1/R) / (1 - 1/R^N).

To prove the formula, the first step is to realize that by using the real rate of return R we can forget about inflation and assume you withdraw the same amount of dollars every year - call it W. Our goal is to start with S dollars, withdraw W every year and end up after N years with exactly 0 dollars. Since we use inflation-adjusted terms, we need to assume that every year, the balance of the portfolio grows by a factor R. 

Each withdrawal has a different amount of time to grow before withdrawn. The first one had no time at all: it cost us exactly W. The second one could grow for a year before it was taken from the account, meaning it actually cost us only W/R out of the original sum we had. The third one grew for two years, costing us W/R², etc. The last withdrawal grew for N-1 years, costing us a meager W/R^N-1.

Denoting P=1/R we see that the total cost of the withdrawals was

S = W + W*P + W*P² + ... + W*P^N-1

Dividing by W  we get

S/W = 1 + P + P² + ... + P^N-1 = (1 - P^N) / (1 - P)

(using geometric summation formula for the last equality.)

But S must also be equal to the original sum with which we started, since we assume that after we finished all the withdrawals we were left with $0. Hence, the Safe Withdrawal ratio SWR is W/S. From here we get:

SWR = W/S = (1 - P) / (1 - P^N) = (1 - 1/R) / (1 - 1/R^N)

QED

PS  bonus exercise: show that when the growth and the inflation converge to the same value (i.e., R tends to 1), SWR converges to 1/N. Explain the result.

3. Safe Withdrawal Rate

Many books about retirement planning have guidelines for calculating how much you need to save. Usually they're pretty good when it comes to estimating your annual expenses, but once you figure out this number, how much savings do you need to have in order not to run out of money before you die?

The best way to avoid outliving your retirement nest-egg is an untimely death. Barring that, you need to take into account many factors that you can't control. The main ones are your longevity (how long you expect to draw on the funds), the expected rate of return of the portfolio and the expected inflation during this period. Churning these numbers should give you the magical Safe Withdrawal Rate (SWR): the amount of money you can withdraw from your portfolio annually (adjusted to inflation) without exhausting it prematurely.

Financial guides usually quote figures between 3% to 5%. This might sound like a small difference, but in terms of the amount you need to save, it makes a huge difference. For example, if you need $90K annually, with SWR of 3% you need a nest-egg of $3M. With SWR of 5% you'll need only $1.8M.

A simple application of high-school math (which I'll show in my next math break blog) demonstrates the connection between these variables:

• The number of years of withdrawing money (N)
• The inflation rate
• The expected portfolio growth rate
• The SWR

First, compute the net projected growth of your account (R), which is the growth divided by inflation. For example, with 8% annual growth (1.08) and 3% inflation (1.03), your expected net growth is R = 1.08 / 1.03 = 1.0485 (or 4.85% annually).

Next, calculate

SWR = (1 - 1/R) / (1 - 1/R^N)

In our example, when assuming 50 years of withdrawals, you'll get 0.051 or 5.1%. A more conservative assumption, say of 6% growth vs. 4% inflation will lead to a SWR of about 3%.

I've calculated for you the SWR for 30 years and 50 years under different assumptions. The results are below.

For 30 years:

Growth	Inflation	SWR
3%	3%	3.3%
4%	3%	3.8%
5%	3%	4.3%
6%	3%	4.9%
7%	3%	5.5%
8%	3%	6.1%
9%	3%	6.7%
10%	3%	7.4%

For 50 years:

Growth	Inflation	SWR
3%	3%	2.0%
4%	3%	2.5%
5%	3%	3.1%
6%	3%	3.7%
7%	3%	4.4%
8%	3%	5.1%
9%	3%	5.8%
10%	3%	6.6%

Note: even though the tables are for 3% inflation only, the SWR roughly depends only on the difference between growth and inflation. For example, the SWR assuming growth of 7% and inflation of 4% is almost the same as with assuming growth of 6% and inflation of 3%. 


The important lesson from these tables is that there's no universal SWR. Your situation, your time horizon and your expectations of the economy will determine your SWR. A very conservative person will assume almost no gain over inflation, leading to SWR close to 1/N. More optimistic people may assume that historic rates of return (around 8%) will rule in the long term. My personal choice is 5% growth with 3% inflation - a very conservative assumption but one that I feel comfortable with in this economy.

In the next blog I'll describe the simple math behind this formula.

2. Where Are The Investors' Yachts?

My old financial consultant suggested a few years ago to move my savings to an actively managed account. In this account, through their infinite wisdom and insight, the brilliant analysts working for that consulting company were going to beat the market and create above-average returns (compared with the S&P benchmark).

I accepted his advice. He's a smart and helpful guy, and he convinced me he knew what he was talking about. For six years I watched my portfolio going up and down like a paper-boat on ocean waves. It ended up about 0.18% above the S&P. Not bad, but was it worth it? Over these years, there were good times ("our guys beat the market!") and bad times ("our guys promised to work harder and make up for this 5% lag behind the S&P"). In fact, an average day in the market could easily offset the entire gain (or loss) of those 6 years.

The only thing that remained constant throughout those turbulent years was the 1% annual management fee.

If you are in a similar situation, here's a question you could ask your financial adviser. "If you guys are so confident in your strategy, let's make a deal: instead of a management fee, I'll pay you half the profits above the S&P 500 when I finally withdraw my account. Deal?"

Do you think they'll take it? After all, this is the strategy they're selling you.

They can't accept this offer, since they know deep in their hearts that they can't beat the market. Of course, they'll have good years and bad years, but on average, all the players in the market make just that - the average. This is the definition of average, after all. And why should the good people who work 12 hours a day at Merrill-Lynch or Goldman Sachs or GM Pension Funds be any better than the good people who manage the Harvard Endowment or run the Magellan Mutual Fund or any other professional portfolio managers?

They're not. John Bogle, in his excellent Little Book of Common Sense Investing tells a story about a customer visiting an investment bank and hearing about how successful they are and how they all have fancy cars, homes and yacht. "Where are the investors yachts?", he asks. Where indeed.

The account managers job is not to help you buy your yacht. Their job is to keep you a customer, and let your account bleed 1% annually until the cows come home or until you see the light, whichever happens first.

This is a weird and unique arrangement. I don't know who came up with this brilliant idea. After all, there's absolutely no relationship between the amount of money they manage to the amount of work they do on your behalf. Why would managing a million dollar be 10 times more expensive than managing $100,000?

To their defense, some of the professional portfolio managers truly believe in active management - the myth that by selecting "winners" over "losers" and timing the market, they can beat the average. They use tools from economics, business management, stochastic analysis and a bunch of "tried and true" ad-hoc measures to assess investments. They compute ratios (like "cash flow divided by inventory squared times price over earnings") - a tool designed for businesses but with dubious rationale for stock selection. The shadiest of them use a branch of witchcraft called Technical Analysis, where, like astrologers, they try to see shapes such as cups and saucers in a stock price graph and figure out whether the spout coming next month is going to point up or down.

As plenty of research has shown, these tools are as effective as monkeys throwing darts at stock market tables. Professional account managers are smarter than monkeys, of course. They have learned that 1% of someone else's money can buy them a yacht. The monkeys, after all, are happy to do the same job for a few bananas.