October 26, 2008 Letters to the Editor

Updated: November 15, 2008.

Annualized compounded stock market returns

I received these questions from Jauhari.

How do we calculate the annualized continuously compounded stock market returns? Can you provide some simple example?

HERE IS MY RESPONSE

Thank you.

The formula is (final balance/initial balance) = (1+annualized rate of return)^(number of years).

When you calculate a total return, you reinvest all dividends.

When you calculate a price-only return, you remove dividends from the calculation.

When you calculate the real, annualized return, you adjust the final balance and initial balance for inflation. You do this by multiplying the (final balance/initial balance) ratio by the initial cost of living index value divided by the final cost of living index value.

To calculate a single year's annual return, you add the dividend yield for that year (which is the dividend amount divided by the initial price) and the capital appreciation, which is the final price divided by the initial price. This is its gain multiplier. Then subtract 1 and convert to a percentage (i.e., multiply by 100%).

To calculate several years return, you multiply all of the gain multipliers together. This product equals the (final balance/initial balance).

As an example, suppose that your investment increases 20% in the first year, increases 10% in the second year, decreases 10% in the third year and increases 30% in the fourth year. The gain multipliers are 1.2, 1.1, 0.9 and 1.3, respectively.

The product of the gain multipliers is 1.5444 (=1.2*1.1*0.9*1.3).

The (final balance/initial balance) = 1.5444.

Since there are four years, (1+annualized rate of return)^4 = 1.5444.

Solving, possibly with logarithms or with the y^x key on a calculator, (1+the annualized rate of return) is 1.114782. The annualized rate of return is 11.4782%.

TIPS are yielding 3%+

I received these comments from Dave.

The reason TIPS are yielding so much is the markets correctly or incorrectly are predicting an approximately 5-6% deflation over about the next 18 months.

With TIPS the inflation factor can be either positive or negative. If it is negative any accumulated inflation factor can decrease. The value will not go below face value regardless of how much deflation there is. Therefore it is best to buy at or near the auction to get either no or low existing inflation factors.

The next auction of the new 10 year TIPS is January 2009.

Regards.

HERE IS MY RESPONSE

Thank you for your excellent, insightful letter.

I believe that much of what we are seeing is the effect of limited liquidity. I believe that some TIPS sales are forced. I do not know the reason. One possibility is that funds need to meet redemptions.

Regardless, I believe that the market is predicting heavy deflation, as you have stated.

I also believe that the market is wrong. The Treasury and the Federal Reserve are letting out all of the stops to prevent deflation.

The principal of TIPS can fall below par ($1000) prior to maturity. The coupon rate applies to the current principal. The coupon interest amount can decrease. The principal of TIPS is reset to par at maturity if it increases the principal amount paid to the investor.

“Relatively Stupid” question

I received this not-so-stupid question from Michael.

Hi John, Michael here.

Just want to be clear on one thing: when I run the Scenario Surfer, a distinction is made between "withdrawals" and "total income" (the latter being the sum of dividends and interest). For purposes of the SWR, is "withdrawals" assumed to include total income? E.g., say a 4% SWR - does that equal withdrawals PLUS total income or simply ANY value that leaves the account, be it in the form of income or sales of securities?

Thanks.

HERE IS MY RESPONSE

Thank you. You have asked an excellent question.

Your income is the withdrawal amount. That is, it is “ANY value that leaves the account, be it in the form of income or sales of securities.”

As you have observed correctly, the “total income” is the amount that the portfolio would throw off in the form of income if you did not sell or buy stocks and bonds (TIPS) beyond shifting allocations. I provide that information as background information for those who would like to avoid touching principal. It gives you a feel for how well a never-touch-principal approach would work.

The “total income” number is not used in any of the Scenario Surfer’s calculations. It is for information only. The internal calculations in the Scenario Surfer are based on total return calculations. It is a Monte Carlos simulation. It includes randomness, restricted by two forms of mean reversion.

My estimate of the dividend amount is a constant percentage of earnings. This turns out to be a good approximation. If it had not turned out that way, I would not have reported it.

I do not simulate the randomness in the dividend payout ratio.

TIPS

I received this question from Ron.

Came across your interesting website today and thought I might ask for some help on buying individual TIP bonds. What criteria must I use when selecting a Tip bond? For example here are 3 from Fidelity website. What should I be looking for coupon, inflation factor, adjusted price etc?

Ron continued by providing three quotes. They were from the secondary market as opposed to an initial purchase.

HERE IS MY RESPONSE

Thank you. You have asked an excellent question. Unfortunately, I do not have the expertise to answer you properly.

I will provide such information as I can.

The first thing I noticed about your quotes was that the Bid and Ask prices were very close to the Adjusted Prices.

The second thing that I noticed was that the prices differed substantially.

The next thing I noticed was that maturity dates were all very similar.

The final thing I noticed was that coupon rates differ substantially.

What I would want to know is the Yield to Maturity. I know that it can be calculated from the information provided. My impression is that it would be very close to 3% for all of the issues shown.

In a taxable account, I would favor buying at a premium since this would decrease the taxable amount that you would pay, but only slightly, for the same income stream. [I am not sure about the details.] I would place a much greater emphasis on the Yield to Maturity.

Dividend Yield

I received these comments from Ryvers.

Your website is terrific- thanks for the wealth of information.

A question that I have had for some time reared its head again as I looked through the dividend yield data (as a means to assess market valuation). Given the increase of stock buybacks in recent years, is dividend yield data today really comparable to that of prior decades? From the dividend yield data, one could argue that the market is still overvalued, but I suspect that adding in stock buybacks would cause the data to tell a different story. One can also argue about the effectiveness of buybacks, but it is a way that companies purport to use excess cash to increase shareholder value.

HERE IS MY RESPONSE

Thanks for an outstanding question.

You are correct. Stock buybacks can be included as a refinement to improve the accuracy of dividend yield information. There have been academic studies along these lines.

Beyond this, the entire area is highly controversial. I prefer not to make an adjustment in my numbers. I leave the refinement to others.

One issue is whether the buyback phenomenon will continue or whether it is simply a sign of a bull market.

Along the same lines is how well investors will accept stock buybacks when prices fall dramatically, as they have recently.

To estimate the magnitude of an adjustment, I use my experience in adjusting stock returns predictions based on increased earnings growth. I believe that any adjustment will be comparable. From that study:

“Assuming that real earnings continue to grow within these ranges, the adjustment at Year 10 is an increase of +1.23% to +2.22%. At Year 20, the adjustment is -0.64% to +0.28%. At Year 30, the adjustment is +0.10% to +0.37%.”

The outer confidence limits at Year 10 are plus and minus 6%. At Year 20, they are plus and minus 4%. At Year 30 they are plus and minus 2%.

Stock Return Predictor with Earnings Growth Rate Adjustment

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