The Investor's Manifesto: Prudence Before Riches

The Investor's Manifesto: preparing for prosperity, Armageddon, and everything in between, by William Bernstein. Rating: 4/5.

A good description of basic investment strategy, written in a familiar, mildly humorous style. Bernstein's approach draws heavily on an investment version of Pascal's wager: Financial ruin in retirement if markets turn south is worse than living modestly (now and in retirement) even if markets are booming. Bernstein advocates for simple, unglamorous investing:

"The name of the game is not to get rich, but rather to avoid dying poor. In fact, if you follow the advice in this book, I can guarantee you that you will not get fabulously wealthy. Rather, I've striven to simultaneously maximize your chances of a comfortable retirement and minimize your chances of living out your final years in poverty. I know of no more laudable or more worthy investment goal." (183)

As a starting point, Bernstein cites the "age rule" for asset allocation: The percentage of bonds in your portfolio should be roughly the same as your age. This percentage should be increased or decreased up to 20 percentage points depending on your risk tolerance. Then, Bernstein recommends between 60-80% domestic stocks and 20-40% foreign stocks, and suggests that money should be placed in low-expense index or passively managed mutual funds. "Does this portfolio seem overly simplistic, even amateurish?" Bernstein asks---"Get over it. Over the next few decades, the overwhelming majority of all professional investors will not be able to beat it" (89). Investors interested in a more complex allocation could divide the stocks into small and large, value and market companies; but, Bernstein indicates that growth companies should be avoided, as they have a small dividend stream relative to stock price, and the dividend growth rate is a better predictor of future performance than growth of stock price.

Chapter 1, "A Brief History of Financial Time," gives an overview of the history of financial markets and lays down a number of important principles of how markets work that undergird Bernstein's investment philosophy. Chapter 2, "The Nature of the Beast," describes the core of the philosophy. Chapter 3, "The Nature of the Portfolio," applies Bernstein's philosophy to creation of a portfolio. Chapter 4, "The Enemy in the Mirror," presents a number of neuro-psychological effects and common mistakes that investors make that derail them from their investing goals. Chapter 5, "Muggers and Worse," warns against brokerage houses and the like. Chapter 6, "Building Your Portfolio," introduces dollar cost averaging and value averaging, and provides four example scenarios of prototypical investors. Finally, chapter 7, "The Nature of the Game," provides a summary of the principal lessons from the book, suitable for sticking to the refrigerator for frequent review.

The book is approachable for beginning investors, though some experience with investment vocabulary is helpful. Important points are placed in call-out boxes, and mathematical details are relegated to sidebars that can be skipped or skimmed without losing the overall message. Each chapter has a bullet-point summary of the most important topics for review.

Graduated Annuity Calculator

I use Google Analytics to keep track of visits to the Cogitorium as a matter of curiosity. When I posted the results of my graduated annuity calculations, I figured most people would respond as my brother did: "Why would you write about something boring like that?" Much to my very great surprise, my entry on the graduated annuity has turned out to be my most popular! Since the beginning of this year, the entry has received nearly one hit per day (which is a lot by my humble standards).

Given the interest in graduated annuities, I thought I would whip up a quick applet to perform calculations with the graduated annuity, since many people might not want to slog through the math on their own. Below are a few usage notes, the applet, and several calculation examples. For those who are interested, the source code is available, and is released into the public domain.

1. The Interest Rate and the Acceleration Rate are entered in percent and cannot be the same.
2. When calculating the Final value, enter a positive Base Value for savings or a negative Base Value (with an Initial Value) for accelerated withdrawals.
3. When calculating either rate, no Initial Value is permitted.
4. Selecting Years calculates the amount of time a given Initial Value will last with accelerated withdrawals. It doesn't work with Final Values other than 0, or with positive Base Deposits.
5. Enter 0 for the Acceleration Rate to calculate a normal annuity.
   

Examples:

1. To calculate the savings of $1000/year (unaccelerated) for 10 years at 5% interest, enter 0 for the Initial Value, 1000 for the Base Deposit, 5 for the Interest Rate, 0 for the Acceleration Rate, and 10 for Years. Pressing calculate gives $12,577.89.
2. Suppose we choose to accelerate the savings in the previous example by 4% each year. Enter 4 for the Acceleration Rate. Pressing calculate shows the savings grow to $14,865.03.
   
3. Suppose we have $10,000 and would like to reach $100,000 in 5 years. How much would need to be saved each year, if we expect an 8% return on the savings? Select the Base Deposit radio button, enter 10000 for the Initial Value, 100000 for the Final Value, 8 for the Interest Rate, 0 for the Acceleration Rate, and 5 for Years. Pressing calculate gives $14,541.08.
4. Suppose we want to reach $100,000 in 10 years. If we start with a $6,000/yr deposit, how fast would the deposits have to accelerate to reach our goal, if we expect an 8% return on the savings? Select the Acceleration Rate radio button, enter 0 for Initial Value, 100000 for Final Value, 6000 for Base Deposit, and 10 for Years. Pressing calculate shows that the deposit amount must increase by 3.6% each year to reach the goal.
5. Suppose we have $500,000 saved for retirement, earning 5% per year. We plan on withdrawing $30,000/yr and would like to increase this amount by 2% each year to account for cost of living increases (price inflation). How much will be left after 10 years? Select the Final Value radio button, and enter 500000 for Initial Value, -30000 for Base Desposit, 5 for Interest Rate, 2 for Acceleration Rate, and 10 for Years. Pressing calculate shows that $404,547.11 will remain.
6. How long will the savings in this scenario last? Select the Years radio button. Pressing calculate shows that the savings will last almost 24 years.
   

Retirement Investment Planning

CNN Money has some helpful advice on where to hold your investments. Ideally, all savings would be in a tax-advantaged account (401k, IRA, etc.); but when the amount you have to invest exceeds the limits for these accounts, give bonds priority to tax-advantaged accounts (starting with a 401k, if you have one), then add stocks. Bonds give off more dividend income, which is directly taxable, so these should be as tax-protected as possible.

This leaves the question: What, exactly, should one buy? They suggest a seven-fund portfolio of stocks, bonds, and money markets (with recommendations for funds in each of the seven categories). While this may be a good goal to work toward, such a diversified portfolio could be difficult to achieve straight off the bat (the cumulative minimum investment is something like $15,000). When I opened my IRA, I took a tip from Adam Bold and started with the Selected American Shares (SLASX). Since then, I've come across suggestions that he may not be the most trusted of advisors, but I think Selected was a good choice, nevertheless: Although it's not likely to impress anyone with record returns, the fund rather consistently beats the S&P 500 and has achieved an annual rate of return over the last 10 years of 8%. As such, the Selected funds seem to me to provide a nice stable base from which to develop a fuller portfolio in the future.

The CNN Money article also included three simple plans for asset allocation between the seven different types. My father once shared a rough rule of thumb for retirement-savings asset allocation: He said that the percentage of stocks in your portfolio should be about 100 minus your age. I was pleased to see that the CNN Money's plans were pretty close: In early career (20s), they allocated 80% stock; in late career (say 40s), they allocated 60% stock; and in retirement (60s), they allocated 40% stock. Of course, it's certainly nice to have the more-detailed suggestion of how much of what kind of stocks and bonds to purchase, which the article provides.

Calculating a Graduated Annuity

(Use the calculator to skip the math below.)

Calculating the future value of a savings program with fixed savings installments and a fixed interest rate (a simple annuity) is fairly straightforward with a geometric series:

To calculate the value after periods, we multiply the last equation by and subtract the result:


So, saving $1,000/year for 10 years at 5% interest would give:


And if we had the goal of saving $100,000 over 30 years with a 8%
interest rate, we could calculate the yearly deposit required:



Now, since the real value of the periodic deposit degrades over time due to inflation, and since one's ability to save will hopefully increase over time due to increased income through cost-of-living increases and promotions, a real-life long-term savings plan will likely include deposits that increase over time (a graduated annuity). These, too, can be represented with a series:


where is the geometric ratio describing the rate of increase (the graduation) of the deposits. This series is similar in form to the binomial series, except that the coefficients in this series are all the same. To solve for the sum, we multiply by and subtract:


Notice how this simplifies to the result for constant deposits, when .

This equation can be rearranged to the elegant form:


When asked to solve for either rate, Mathematica complained that this equation involves variables in "an essentially non-algebraic way," which I found a bit odd. Nevertheless, to determine the interest rate necessary to achieve a given sum with a set rate of deposit graduation (or vice versa), one can evaluate one side of the equation, move the resulting constant to the other side, and calculate the positive real roots of the n-th degree polynomial.

In any case, after 10 years, a savings program that begins at $1,000/year
and increases by 4% each year with 8% interest would give:



This equation is also useful for determining savings left after a series of increasing withdraws. If one starts with $500,000 in retirement savings invested at 5%, taking a 2% inflation-adjusted $30,000 annuity for 5 years would leave:



One can rearrange the formula to achieve a somewhat unwieldy but functional equation for the number of years before the retirement savings will run out:


So, to find out how long the $500,000 investment from the previous example will last:



All of these calculations assume that payments occur at the end of the year (an ordinary annuity). The calculations for payments at the beginning of the year (an annuity due) are equally straightforward, and yield: