To access the pdf version of this document, please click the following link:
Retirement Income Analysis
This blog covers alternative ways to provide income for individuals or couples in the period typically referred to as the "retirement years". In large part it will extend the material covered in my ebook Retirement Income Analysis with Scenario Matrices and the accompanying matlab software, available at my Stanford website www.stanford.edu/~wfsharpe. To see titles of prior blogs, click the triangle next to a month in the section below. To see a blog, click its title.
About Me
 William Sharpe
 I am STANCO 25 Professor of Finance, Emeritus at Stanford University and a recipient of the 1990 Nobel Prize in Economic Sciences. More than you will ever want to know about me can be found at my Stanford web site: www.stanford.edu/~wfsharpe
To see titles of prior posts, click the triangle by the month. To then see a post, click its title.
Thursday, March 25, 2021
Saturday, October 10, 2020
Covid Statistics
And now for something completely different.
This slidecast covers some of the key statistics that are being widely used to measure and try to control the pandemic in 2020 caused by the covid19 virus.
To access it, click the link below.
Wednesday, September 30, 2020
Annuity Terms
As the previous post indicated, henceforth some of my posts will provide links to documents in the .pdf format in lieu of including the covered material in a post. But some posts will provide instead links to slidecasts that I have created using the scratch programming language developed at M.I.T..
The term slidecast is an abbreviation for slide podcast. The goal is to combine both visual information in a form similar to that in a slide presentation with audio information in a form similar to that of a podcast.
The programs that I have written for this purpose are compatible with many computer browsers. They can also be used on some other devices such as cell phones, tablets, etc.. With computer browsers, it is possible to choose to have the narration in English, French or Spanish. However, for devices without keyboards, only English is available.
The first slidecast covers annuity terms.
The terms offered by insurance companies and others who provide annuities change from time to time. In recent years there has been a substantial decrease in the amount of future income that can be purchased for a given current payment. This slidecast shows some of the changes in annuity terms and the driving force behind them. To access it, click on this link:
https://scratch.mit.edu/projects/420792251
Saturday, August 8, 2020
SCHP: A Schwab TIPS ETF
Please click this link for the pdf version: Post 8
Thursday, July 16, 2020
Treasury InflationProtected Securities (TIPS) in the first half of 2020
At any given time there are TIPS outstanding with different times to maturity. For each one, a real yield to maturity can be calculated based on its current market price and future guaranteed coupon and principal payments. At its web site for Daily Treasury Real Yield Curve Rates, the U.S. Treasury provides yields to maturity for five different maturities (5, 7, 10, 20 and 30, years). Here is a link:
The following graph shows the rates for each market date in 2020 through July 10, 2020.
Throughout this period, longer maturity bonds provided higher yields to maturity than those with shorter maturities. In bond jargon: the real yield curve was upwardsloping. That said, there were days when the differences among yields with different maturities was very small indeed, but at other times they differed significantly. In most months there was a downward trend in yields at each maturity. But there was one major exception: in the middle of March, yields changed from negative values to positive values, reflecting significant declines in the prices of the underlying bonds. The reason is not hard to guess. The gravity of the Covid19 pandemic was becoming apparent at the time and prices of securities of many types fell dramatically. TIPS were no exception. However, the panic did not last very long. By the early part of April, TIPS prices were near their values a month earlier and thus yields to maturity were back to previous levels. Thereafter, as the second quarter progressed, yields continued to fall, reflecting rising prices for the securities.
But there is more drama here. At the beginning of the year, TIPS with shorter maturities provided almost no real yield, but those with longer maturities provided at least some increases in purchasing power. Later, yields fell and turned to negative values. In early July the yield to maturity on 5year TIPS was close to 1% per year and those of every maturity were priced to provide negative real yields to maturity. Thus for any time period up 30 years, an investor in TIPS could plan on receiving less purchasing power than he or she invested.
Forward yields
While the yields to maturity tell the story of longterm returns from TIPS, it is useful to do some additional calculations to obtain estimates of “forward yields”. Consider two TIPS – one maturing in five years, the other in seven years. Think of the latter as composed of two investments: the first requires investment today and pays off in five years. The second requires a “forward” commitment today to invest a dollar in five years and will then pay off two years later in year seven. Assuming no coupon payments and using subscripts to denote the initial year and the final year for an investment we can write the relationship among two standard yields to maturity and a forward yield to maturity as:
(1+y_{05})^{5 }(1+y_{57})^{2} = (1+y_{07})^{7}
The first and last expressions use the types of yieldstomaturity that are provided on the Treasury website and plotted in our diagram – these are sometimes called spot rates. The second term includes a forward rate for a commitment made today to invest in year 5 to obtain a payment in year 7. Obviously it is a simple matter to compute the forward rate, given the two spot rates. The following diagram shows the results of such calculations for each of the combinations of adjacent spot rates in the previous diagram. For completeness, the spot rates for years 0 through 5 are also shown.
If each TIPS paid only at maturity, it would be possible to actually achieve the forward rate for an interval. For example, one could invest in a 7year TIPS with the proceeds from selling short a 5year TIPS. This would require a known future payment in 5 years for the short position and provide a known future receipt in 7 years for the long position. The net result would earn the the forward rate for years 5 to 7. Unfortunately, the actual world is not that simple since actual TIPS provide coupon payments every six months. It is true that from time to time an institutional investor or broker will purchase a TIPS and sell one claim for its coupon payments and another for its principal payment at maturity (a “stripped TIPS”) which will be equivalent to a zerocoupon TIPS. But such exotica are generally not available for individual investors. The bottom line is that the forward TIPS yields can best be interpreted as indicators rather than explicitly achievable investments.
To see how derived forward rates can be useful, consider the 7year TIPS on July 10, the last year in our example. The yield to maturity was 0.87% per year. It would be natural to think of the security as providing 0.87% per year for seven years. But wait. The yield on a 5year TIPS at the time was 0.95% and the forward rate for years 5 through 7 was 0.67%. It might be more useful to think of the 7year TIPS as providing 0.95% on average for five years, then 0.67% on average for another two years. Of course, if we had used data for TIPS with maturities in years 1, 2, 3, 4, 5, 6 and 7 we could have broken the overall yield into even more pieces. Those interested in making such detailed calculations can find current TIPS quotes at https://www.barrons.com/marketdata/bonds/tips.
But why calculate forward rates at all? One answer is that they might be useful predictors of future spot rates. But not perfectly so since the forward rate for a future interval of time may reflect both a forecast of spot rates at that time and a premium for taking the risk of making a commitment to invest at a future date. Thus a forward rate might be greater than predictions of the associated future spot rates. If so, these data suggest that on July 10 2020, TIPS yields suggested that investors expected negative relatively riskless real rewards for deferring consumption for decades into the future.
To provide some perspective, here is a longer record of yields to maturity on 10year TIPS, from the Federal Reserve Bank of St. Louis FRED site (https://fred.stlouisfed.org/series/WFII10):
As can be seen, 10year TIPS yields have been negative before (mainly in 2012) but turned positive thereafter until 2020. We can only hope that this might happen again.
In any event given current TIPS rates, retirees need more savings than before to achieve any given future standard of living with certainty. Some will respond to this fact by saving more and/or spending less today. Others may decide that saving is less attractive and spend more than previously intended. Moreover, the latter tendency may be encouraged as well by the pandemic (“eat, drink and be merry, for tomorrow you die”). One might argue that relatively few investors are following this advice since if more did, TIPS prices would be lower and thus yields to maturity higher. But here, as always, it is important to remember that prices in security markets are influenced disproportionately by the rich.
One thing is certain: current TIPS yields are far lower than in most earlier times. All the examples in my ebook on Retirement Income Analysis used computations that assumed a riskless real rate of return of 1% for all maturities with a return premium for bearing the risk of a world bond/stock portfolio. Of course the accompanying RISMAT software makes it easy for the user to change either or both of these numbers since they are simply properties of a market object.
But in a world of low or negative riskless real rates of return, some retirees may conclude that if they survive COVID, they might well run out of money thereafter.
Other than that, have a nice day!

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To access the pdf version of this document, please click the following link: WorldBondsAndStocks2020