The Mathematics of Retirement Investing

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bigred77
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Re: The Mathematics of Retirement Investing

Post by bigred77 » Wed Aug 16, 2017 7:16 pm

North Texas Cajun wrote:
Wed Aug 16, 2017 6:56 pm
bigred77 wrote:
Wed Aug 16, 2017 4:09 pm
Well we know the efficient frontier typically curves, correct (or at least do most of us accept that)? At the extreme end, going from 100/0 to 90/10 in AA typically sees a greater jump in sharp ratio than going from 60/40 to 50/50. The more equity heavy my portfolio is the more volatility I can cut and the lower my reduction in expected returns are by moving that marginal 10% of the portfolio from equities to bonds?
I think the Sharpe ratio for a 100/0 portfolio changes dramatically as the horizon extends from, say, 5 years to 25 or 30 years. Isn't that right? The standard deviation for such a portfolio comes way down. In his book, "Stocks for the Long Run", Jeremy Siegel shows that the SD for real U.S. Equity returns drops from 18% to 7.5% to 1.8% as the horizon extends from 1 to 5 to 30 years. At that SD, are you sure you can cut very much volatility by moving from stocks to bonds?
My comment is in regards to whatever time frame you choose, as long as it's held constant between portfolios. I'm not talking about specific time periods (I.E. not sharp ratios from 1992 to 2004) but rather time frames (I.E. sharp ratios over rolling 12 year periods).

My understanding is Sharp ratios over 15 year time periods are better for 90/10 than 100/0. Same with 20, 25, etc. You consistently see "the biggest bang for your buck" in terms of percentage reduction in volatility vs percentage reduction in observed returns for a rebalanced portfolio that start at extreme equity percentages (100/0) and move down the efficient frontier.

At extremes, it's cheap to reduce volatility. As your AA becomes more balanced, the cost of volatility reduction rises.

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willthrill81
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Re: The Mathematics of Retirement Investing

Post by willthrill81 » Wed Aug 16, 2017 7:36 pm

bigred77 wrote:
Wed Aug 16, 2017 7:16 pm
North Texas Cajun wrote:
Wed Aug 16, 2017 6:56 pm
bigred77 wrote:
Wed Aug 16, 2017 4:09 pm
Well we know the efficient frontier typically curves, correct (or at least do most of us accept that)? At the extreme end, going from 100/0 to 90/10 in AA typically sees a greater jump in sharp ratio than going from 60/40 to 50/50. The more equity heavy my portfolio is the more volatility I can cut and the lower my reduction in expected returns are by moving that marginal 10% of the portfolio from equities to bonds?
I think the Sharpe ratio for a 100/0 portfolio changes dramatically as the horizon extends from, say, 5 years to 25 or 30 years. Isn't that right? The standard deviation for such a portfolio comes way down. In his book, "Stocks for the Long Run", Jeremy Siegel shows that the SD for real U.S. Equity returns drops from 18% to 7.5% to 1.8% as the horizon extends from 1 to 5 to 30 years. At that SD, are you sure you can cut very much volatility by moving from stocks to bonds?
My comment is in regards to whatever time frame you choose, as long as it's held constant between portfolios. I'm not talking about specific time periods (I.E. not sharp ratios from 1992 to 2004) but rather time frames (I.E. sharp ratios over rolling 12 year periods).

My understanding is Sharp ratios over 15 year time periods are better for 90/10 than 100/0. Same with 20, 25, etc. You consistently see "the biggest bang for your buck" in terms of percentage reduction in volatility vs percentage reduction in observed returns for a rebalanced portfolio that start at extreme equity percentages (100/0) and move down the efficient frontier.

At extremes, it's cheap to reduce volatility. As your AA becomes more balanced, the cost of volatility reduction rises.
From 1972 to current, the Sharpe ratio was highest for the 30/70 AA (at least for TSM and ITT). That resulted in a CAGR of 8.48%, compared to 10.30% for 100% TSM.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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ray.james
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Re: The Mathematics of Retirement Investing

Post by ray.james » Wed Aug 16, 2017 7:52 pm

North Texas Cajun wrote:
Wed Aug 16, 2017 6:06 pm
longinvest wrote:
Wed Aug 16, 2017 2:17 pm
Dear Fozzy fosbourne,

This thread is not about the advantages and drawbacks of a 60:40 portfolio against a 100:0 portfolio. We went over that, earlier in this thread. You're welcome to read earlier posts and discover why I am insisting to keep such a discussion for other threads.

This thread is about reasonably quantifying the "cost" of using a 60:40 portfolio during the accumulation period.

I my last post, I was just explaining that it would be unfair to compare this "cost" to a high expense ratio.

Thanks for your understanding.
Longinvest,

I really do not understand why you continue to scold folks about this. You were the person who initiated the comparison of a 60/40 and 100/0 portfolios in this thread. You described the all equity portfolio as reckless. Given that statement from you, why is it not appropriate for someone else to point out the relative advantages and disadvantages of the two portfolios?

One more thing I do not understand: is there some unwritten or written rule that gives to the OP the right to control where a discussion leads on a post he initiates? If someone else believes
a point is relevant to the discussion, does the OP automatically become a moderator?
I am not speaking for longinvest but the way I grasped this thread is one can replace the bonds with CDS for just 4.9% yield instead of 60/40 yield. The major point being the net higher savings required is much smaller than what people perceive. One can accept much lower risk if they choose to with relatively small sacrifices for a "much small than imaginable" savings rate increase.

The fact it is 60/40 is only for demonstration of the idea to use some real numbers from what I understand. It can be any combination of asset classes. The only assumption is an arbitrary higher returns with increasing risk...which is a fair one. The thread is partially on behavioral pitfalls of investors and their risk choices based on preconceived notions.
When in doubt, http://www.bogleheads.org/forum/viewtopic.php?f=1&t=79939

North Texas Cajun
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Re: The Mathematics of Retirement Investing

Post by North Texas Cajun » Wed Aug 16, 2017 8:07 pm

ray.james wrote:
Wed Aug 16, 2017 7:52 pm
North Texas Cajun wrote:
Wed Aug 16, 2017 6:06 pm
longinvest wrote:
Wed Aug 16, 2017 2:17 pm
Dear Fozzy fosbourne,

This thread is not about the advantages and drawbacks of a 60:40 portfolio against a 100:0 portfolio. We went over that, earlier in this thread. You're welcome to read earlier posts and discover why I am insisting to keep such a discussion for other threads.

This thread is about reasonably quantifying the "cost" of using a 60:40 portfolio during the accumulation period.

I my last post, I was just explaining that it would be unfair to compare this "cost" to a high expense ratio.

Thanks for your understanding.
Longinvest,

I really do not understand why you continue to scold folks about this. You were the person who initiated the comparison of a 60/40 and 100/0 portfolios in this thread. You described the all equity portfolio as reckless. Given that statement from you, why is it not appropriate for someone else to point out the relative advantages and disadvantages of the two portfolios?

One more thing I do not understand: is there some unwritten or written rule that gives to the OP the right to control where a discussion leads on a post he initiates? If someone else believes
a point is relevant to the discussion, does the OP automatically become a moderator?
I am not speaking for longinvest but the way I grasped this thread is one can replace the bonds with CDS for just 4.9% yield instead of 60/40 yield. The major point being the net higher savings required is much smaller than what people perceive. One can accept much lower risk if they choose to with relatively small sacrifices for a "much small than imaginable" savings rate increase.

The fact it is 60/40 is only for demonstration of the idea to use some real numbers from what I understand. It can be any combination of asset classes. The only assumption is an arbitrary higher returns with increasing risk...which is a fair one. The thread is partially on behavioral pitfalls of investors and their risk choices based on preconceived notions.
I understand what longinvest intended to talk about in his OP. But he then, in the second comment after his OP, pointed out that a 100/0 portfolio was a reckless risk. At that point, this thread became, IMO, more than just a demonstration exercise.

I disagree that a 100/0 portfolio represents an increased risk over a 60/40 portfolio - for the buy and hold investor with a 25 to 30 year horizon.

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Re: The Mathematics of Retirement Investing

Post by North Texas Cajun » Wed Aug 16, 2017 8:18 pm

willthrill81 wrote:
Wed Aug 16, 2017 7:36 pm
From 1972 to current, the Sharpe ratio was highest for the 30/70 AA (at least for TSM and ITT). That resulted in a CAGR of 8.48%, compared to 10.30% for 100% TSM.
Can you explain what those ratios represent? Are those the Sharpe ratios for 1 year returns over that period? for 10 year returns? for 20 year returns?

One can derive standard deviations - and thus Sharpe ratios - for 540 monthly returns or 45 annual returns or 41 five year teturns over that period. For the buy and hold investor, those are all just noise, and probably not very important.

bigred77
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Re: The Mathematics of Retirement Investing

Post by bigred77 » Wed Aug 16, 2017 8:33 pm

willthrill81 wrote:
Wed Aug 16, 2017 7:36 pm
bigred77 wrote:
Wed Aug 16, 2017 7:16 pm
North Texas Cajun wrote:
Wed Aug 16, 2017 6:56 pm
bigred77 wrote:
Wed Aug 16, 2017 4:09 pm
Well we know the efficient frontier typically curves, correct (or at least do most of us accept that)? At the extreme end, going from 100/0 to 90/10 in AA typically sees a greater jump in sharp ratio than going from 60/40 to 50/50. The more equity heavy my portfolio is the more volatility I can cut and the lower my reduction in expected returns are by moving that marginal 10% of the portfolio from equities to bonds?
I think the Sharpe ratio for a 100/0 portfolio changes dramatically as the horizon extends from, say, 5 years to 25 or 30 years. Isn't that right? The standard deviation for such a portfolio comes way down. In his book, "Stocks for the Long Run", Jeremy Siegel shows that the SD for real U.S. Equity returns drops from 18% to 7.5% to 1.8% as the horizon extends from 1 to 5 to 30 years. At that SD, are you sure you can cut very much volatility by moving from stocks to bonds?
My comment is in regards to whatever time frame you choose, as long as it's held constant between portfolios. I'm not talking about specific time periods (I.E. not sharp ratios from 1992 to 2004) but rather time frames (I.E. sharp ratios over rolling 12 year periods).

My understanding is Sharp ratios over 15 year time periods are better for 90/10 than 100/0. Same with 20, 25, etc. You consistently see "the biggest bang for your buck" in terms of percentage reduction in volatility vs percentage reduction in observed returns for a rebalanced portfolio that start at extreme equity percentages (100/0) and move down the efficient frontier.

At extremes, it's cheap to reduce volatility. As your AA becomes more balanced, the cost of volatility reduction rises.
From 1972 to current, the Sharpe ratio was highest for the 30/70 AA (at least for TSM and ITT). That resulted in a CAGR of 8.48%, compared to 10.30% for 100% TSM.
From memory that sounds correct. And if I had the ability to borrow at the risk free rate without call risk or concerns about the debt service risk, I would lever a 30/70 portfolio to match my risk tolerance (or my best estimate of it anyway) in a heart beat. But in reality I can't. So I take risk more inefficiently by adding more equities, but still putting at least some value on portfolio efficiency.

My point was that over that same time period, you should see a higher percentage gain in sharp ratio going from 100/0 to 90/10 than you will from 80/20 to 70/30 or 60/40 to 50/50. Efficiency becomes more costly away from the extreme.


I think the fundamental difference here is valueing portfolio volatility. The cost of going from 100% equities to adding bonds in terms of absolute returns is small in contrast to the reduction you are buying in reduced portfolio volatility to those us who actually place value on that result. If you are focused on absolute returns only without any concern for volatility or max draw downs, then any cost at all seems like waste. Why pay anything for something you don't want or care about?

bigred77
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Re: The Mathematics of Retirement Investing

Post by bigred77 » Wed Aug 16, 2017 8:40 pm

North Texas Cajun wrote:
Wed Aug 16, 2017 8:07 pm

I disagree that a 100/0 portfolio represents an increased risk over a 60/40 portfolio - for the buy and hold investor with a 25 to 30 year horizon.
That's pretty much demonstrably wrong if we're using anything remotely resembling the commonly accepted definition of "risk".

I assume in your statement you are using "risk" to mean the chance that a 100% equities portfolio could possibly have a lower final balance than a 60/40 portfolio after 25-30 years. That is also wrong. We can cherry pick dates to show it. Bonds have beaten equities over 30 years on occasion. We all admit it's an extremely unlikely event to occur, but it's absolutely possible.

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willthrill81
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Re: The Mathematics of Retirement Investing

Post by willthrill81 » Wed Aug 16, 2017 9:31 pm

North Texas Cajun wrote:
Wed Aug 16, 2017 8:18 pm
willthrill81 wrote:
Wed Aug 16, 2017 7:36 pm
From 1972 to current, the Sharpe ratio was highest for the 30/70 AA (at least for TSM and ITT). That resulted in a CAGR of 8.48%, compared to 10.30% for 100% TSM.
Can you explain what those ratios represent? Are those the Sharpe ratios for 1 year returns over that period? for 10 year returns? for 20 year returns?

One can derive standard deviations - and thus Sharpe ratios - for 540 monthly returns or 45 annual returns or 41 five year teturns over that period. For the buy and hold investor, those are all just noise, and probably not very important.
Those are Sharpe ratios for the entire period.

I do not put much stock in Sharpe ratios, risk-adjusted returns, or the efficient frontier for several reasons, one of which is that the most 'efficient' return could easily be one that barely beats inflation. Who cares about efficiency of returns if those returns do not help you meet your investment goals?
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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willthrill81
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Re: The Mathematics of Retirement Investing

Post by willthrill81 » Wed Aug 16, 2017 9:35 pm

bigred77 wrote:
Wed Aug 16, 2017 8:40 pm
North Texas Cajun wrote:
Wed Aug 16, 2017 8:07 pm

I disagree that a 100/0 portfolio represents an increased risk over a 60/40 portfolio - for the buy and hold investor with a 25 to 30 year horizon.
That's pretty much demonstrably wrong if we're using anything remotely resembling the commonly accepted definition of "risk".
I wouldn't necessarily say that. I would advise you to take a look at Jeremy Siegel's work, which indicates that across time and geography, not just recent U.S. history, there is a very real risk that bonds will fall behind inflation. They have done so many times in the past. By comparison, over the long-term, stocks are one of, if not the, best hedge against inflation for a variety of reasons.

So if you define risk as the likelihood of losing inflation-adjusted capital, stocks may very well be superior over long-term periods, hence, 100/0 is less 'risky' than 60/40.

The problem with just saying 'risk' is that it can take so many forms.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

bigred77
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Re: The Mathematics of Retirement Investing

Post by bigred77 » Wed Aug 16, 2017 10:25 pm

willthrill81 wrote:
Wed Aug 16, 2017 9:35 pm
bigred77 wrote:
Wed Aug 16, 2017 8:40 pm
North Texas Cajun wrote:
Wed Aug 16, 2017 8:07 pm

I disagree that a 100/0 portfolio represents an increased risk over a 60/40 portfolio - for the buy and hold investor with a 25 to 30 year horizon.
That's pretty much demonstrably wrong if we're using anything remotely resembling the commonly accepted definition of "risk".
I wouldn't necessarily say that. I would advise you to take a look at Jeremy Siegel's work, which indicates that across time and geography, not just recent U.S. history, there is a very real risk that bonds will fall behind inflation. They have done so many times in the past. By comparison, over the long-term, stocks are one of, if not the, best hedge against inflation for a variety of reasons.


So if you define risk as the likelihood of losing inflation-adjusted capital, stocks may very well be superior over long-term periods, hence, 100/0 is less 'risky' than 60/40.

The problem with just saying 'risk' is that it can take so many forms.
Well if we do define "risk" as the likelihood of losing inflation-adjusted capital, I'd suggest the best way to minimize that over the next 30 years is to use 100% TIPS. You've now minimized the risk to that equal to the default risk of the US government. Stocks are really unlikely to have negative real returns over 3 decades, but it's certainly possible.

Now that's a risk that can be talked about, but it's not typically what we are discussing when we use the generic term "risk" or "risky" without a qualifier. We are typically referring to volatility, max draw downs, permanent loss of capital, or the kurtosis of the expected return distribution for an asset or portfolio. For all of those definitions of "risk" a 100% equity portfolio is riskier than 60/40 portfolio. The fact that it's riskier, is precisely why we expect it's absolute returns to be better as well.

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Re: The Mathematics of Retirement Investing

Post by North Texas Cajun » Thu Aug 17, 2017 12:53 am

bigred77 wrote:
Wed Aug 16, 2017 8:40 pm
North Texas Cajun wrote:
Wed Aug 16, 2017 8:07 pm

I disagree that a 100/0 portfolio represents an increased risk over a 60/40 portfolio - for the buy and hold investor with a 25 to 30 year horizon.
That's pretty much demonstrably wrong if we're using anything remotely resembling the commonly accepted definition of "risk".

I assume in your statement you are using "risk" to mean the chance that a 100% equities portfolio could possibly have a lower final balance than a 60/40 portfolio after 25-30 years. That is also wrong. We can cherry pick dates to show it. Bonds have beaten equities over 30 years on occasion. We all admit it's an extremely unlikely event to occur, but it's absolutely possible.
I was comparing the standard deviation of the annualized returns of US equities and government T bonds over the past 200 years. As Professor Jeremy Siegel showed in his book, "Stocks for the Long Run", the standard deviation of annualized returns for equities drops from 18% for one year periods to under 2% for 30 year periods. The standard deviation for T bonds was 8+% for one year periods and 2+% for 30 year periods.

Siegel showed that for holding periods of 20 years and 30 years, U.S. Equity returns have had lower standard deviations than T bonds returns.

Because the standard deviation of returns for an all equity portfolio held for 20 or 30 years has been lower than that for bonds, and because an all equity portfolio is far more likely to have higher returns, I do not believe an all equity portfolio to be risky for a buy and hold investor with a 20 or 30 year horizon.

It is possible that a 60/40 portfolio could have a lower standard deviation of 30 year returns. I do not have the data for that. The efficient frontier line for 30 year returns in Dr. Siegel's book seems to show the standard deviations are the same, with the SD for 70/30 and 80/20 portfolios just barely lower - lower by less than 1/10 of 1 percent.

You may not accept the historical SD's of 30 year returns to be an acceptable definition of risk for a long term investor. I think that is the most appropriate measure.

We can derive historical Sharpe ratios for daily returns, monthly returns, annual returns, ten year returns, or thirty year returns. As I see it, anything based on less than 10 year rolling periods should be considered noise for the long term investor. The Sharpe ratio is probably higher for the 60/40 portfolio when using ten year rolling periods but lower for 30 year returns.

North Texas Cajun
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Re: The Mathematics of Retirement Investing

Post by North Texas Cajun » Thu Aug 17, 2017 1:13 am

bigred77 wrote:
Wed Aug 16, 2017 10:25 pm
willthrill81 wrote:
Wed Aug 16, 2017 9:35 pm
bigred77 wrote:
Wed Aug 16, 2017 8:40 pm
North Texas Cajun wrote:
Wed Aug 16, 2017 8:07 pm

I disagree that a 100/0 portfolio represents an increased risk over a 60/40 portfolio - for the buy and hold investor with a 25 to 30 year horizon.
That's pretty much demonstrably wrong if we're using anything remotely resembling the commonly accepted definition of "risk".
I wouldn't necessarily say that. I would advise you to take a look at Jeremy Siegel's work, which indicates that across time and geography, not just recent U.S. history, there is a very real risk that bonds will fall behind inflation. They have done so many times in the past. By comparison, over the long-term, stocks are one of, if not the, best hedge against inflation for a variety of reasons.


So if you define risk as the likelihood of losing inflation-adjusted capital, stocks may very well be superior over long-term periods, hence, 100/0 is less 'risky' than 60/40.

The problem with just saying 'risk' is that it can take so many forms.
Well if we do define "risk" as the likelihood of losing inflation-adjusted capital, I'd suggest the best way to minimize that over the next 30 years is to use 100% TIPS. You've now minimized the risk to that equal to the default risk of the US government. Stocks are really unlikely to have negative real returns over 3 decades, but it's certainly possible.

Now that's a risk that can be talked about, but it's not typically what we are discussing when we use the generic term "risk" or "risky" without a qualifier. We are typically referring to volatility, max draw downs, permanent loss of capital, or the kurtosis of the expected return distribution for an asset or portfolio. For all of those definitions of "risk" a 100% equity portfolio is riskier than 60/40 portfolio. The fact that it's riskier, is precisely why we expect it's absolute returns to be better as well.
I hope you are acknowledging that short term volatility of returns is not the only risk. Inflation risk was a big problem for bonds in the middle of the 20th century.

With respect to TIPs, I agree that inflation risk should be zero. However, we really do not know what real returns we can expect from TIPs going forward, do we? Currently those real returns are considerably below the values in the example of the OP, and nearly a full percent below the value longinvest says he uses for planning. It seems reasonable that TIPs returns will continue to be well below the returns for T bonds.

bigred77
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Re: The Mathematics of Retirement Investing

Post by bigred77 » Thu Aug 17, 2017 8:27 am

North Texas Cajun wrote:
Thu Aug 17, 2017 12:53 am

I was comparing the standard deviation of the annualized returns of US equities and government T bonds over the past 200 years. As Professor Jeremy Siegel showed in his book, "Stocks for the Long Run", the standard deviation of annualized returns for equities drops from 18% for one year periods to under 2% for 30 year periods. The standard deviation for T bonds was 8+% for one year periods and 2+% for 30 year periods.

Siegel showed that for holding periods of 20 years and 30 years, U.S. Equity returns have had lower standard deviations than T bonds returns.

Because the standard deviation of returns for an all equity portfolio held for 20 or 30 years has been lower than that for bonds, and because an all equity portfolio is far more likely to have higher returns, I do not believe an all equity portfolio to be risky for a buy and hold investor with a 20 or 30 year horizon.

It is possible that a 60/40 portfolio could have a lower standard deviation of 30 year returns. I do not have the data for that. The efficient frontier line for 30 year returns in Dr. Siegel's book seems to show the standard deviations are the same, with the SD for 70/30 and 80/20 portfolios just barely lower - lower by less than 1/10 of 1 percent.

You may not accept the historical SD's of 30 year returns to be an acceptable definition of risk for a long term investor. I think that is the most appropriate measure.

We can derive historical Sharpe ratios for daily returns, monthly returns, annual returns, ten year returns, or thirty year returns. As I see it, anything based on less than 10 year rolling periods should be considered noise for the long term investor. The Sharpe ratio is probably higher for the 60/40 portfolio when using ten year rolling periods but lower for 30 year returns.
In regards to the bolded, yes I think volatility is an appropriate measure of risk but now I think I see why we aren't seeing eye to eye. I am referring to volatility of a portfolio throughout the entire 30 year period. I'm describing the ups and downs of the behavior. You are referring to volatility of a portfolio only at the end of 30 years. You are referring to volatility strictly as a measure of how close observed returns cluster around the mean of the sample at the end of a defined time frame.

Consider a 0 coupon bond that matures in 30 years (issued by the US government and I am assuming no default risk for the sake of simplicity). A STRIP that one can actually go buy today in the market if they want. You pay X for it today. No interest payments are made over 30 years. In 30 years the US government pays you exactly the par value in nominal terms. That bond has a big duration and is subject to interest rate risk. As interest rates change over the next 30 years the market value of that bond can swing up and down. That bond has volatility. It is definitely not a straight line growth chart. At the end of 30 years I get paid par value. That nominal value was never in doubt. At the maturity date, if I plot the probability distribution on a graph, there just a single vertical line that shows 100% on the nominal par value. The standard deviation of that probability distribution is 0. You are saying that bond has no volatility and is 0 risk for the long term investor. I am saying that bond does in fact carry risk and contains volatility. I think that is the disagreement we are having.


All else being equal, I generally defer to the maxims that risk and return are linked and there is no free lunch in investing except diversification. I accept 100% equity portfolios will beat 60/40 portfolios over long periods of time the vast, vast majority of the time. This is because they are riskier. There is a lot of consensus on this side of the argument. Volatility in the short term (over months, years, decades, etc.) SHOULD matter in my opinion, even to the long term investor with the 30 year horizon. You disagree and that's fine, but I think it would be a good idea in the future for you to pre-define how you are using the terms "risk" and "volatility" because you are assigning meanings to those terms that are contrary to the commonly accepted meanings.

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randomizer
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Re: The Mathematics of Retirement Investing

Post by randomizer » Thu Aug 17, 2017 8:55 am

Amazing thread. Thank you.
87.5:12.5, EM tilt — HODL the course!

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Re: The Mathematics of Retirement Investing

Post by North Texas Cajun » Thu Aug 17, 2017 9:14 am

bigred77 wrote:
Thu Aug 17, 2017 8:27 am
North Texas Cajun wrote:
Thu Aug 17, 2017 12:53 am

I was comparing the standard deviation of the annualized returns of US equities and government T bonds over the past 200 years. As Professor Jeremy Siegel showed in his book, "Stocks for the Long Run", the standard deviation of annualized returns for equities drops from 18% for one year periods to under 2% for 30 year periods. The standard deviation for T bonds was 8+% for one year periods and 2+% for 30 year periods.

Siegel showed that for holding periods of 20 years and 30 years, U.S. Equity returns have had lower standard deviations than T bonds returns.

Because the standard deviation of returns for an all equity portfolio held for 20 or 30 years has been lower than that for bonds, and because an all equity portfolio is far more likely to have higher returns, I do not believe an all equity portfolio to be risky for a buy and hold investor with a 20 or 30 year horizon.

It is possible that a 60/40 portfolio could have a lower standard deviation of 30 year returns. I do not have the data for that. The efficient frontier line for 30 year returns in Dr. Siegel's book seems to show the standard deviations are the same, with the SD for 70/30 and 80/20 portfolios just barely lower - lower by less than 1/10 of 1 percent.

You may not accept the historical SD's of 30 year returns to be an acceptable definition of risk for a long term investor. I think that is the most appropriate measure.

We can derive historical Sharpe ratios for daily returns, monthly returns, annual returns, ten year returns, or thirty year returns. As I see it, anything based on less than 10 year rolling periods should be considered noise for the long term investor. The Sharpe ratio is probably higher for the 60/40 portfolio when using ten year rolling periods but lower for 30 year returns.
In regards to the bolded, yes I think volatility is an appropriate measure of risk but now I think I see why we aren't seeing eye to eye. I am referring to volatility of a portfolio throughout the entire 30 year period. I'm describing the ups and downs of the behavior. You are referring to volatility of a portfolio only at the end of 30 years. You are referring to volatility strictly as a measure of how close observed returns cluster around the mean of the sample at the end of a defined time frame.

Consider a 0 coupon bond that matures in 30 years (issued by the US government and I am assuming no default risk for the sake of simplicity). A STRIP that one can actually go buy today in the market if they want. You pay X for it today. No interest payments are made over 30 years. In 30 years the US government pays you exactly the par value in nominal terms. That bond has a big duration and is subject to interest rate risk. As interest rates change over the next 30 years the market value of that bond can swing up and down. That bond has volatility. It is definitely not a straight line growth chart. At the end of 30 years I get paid par value. That nominal value was never in doubt. At the maturity date, if I plot the probability distribution on a graph, there just a single vertical line that shows 100% on the nominal par value. The standard deviation of that probability distribution is 0. You are saying that bond has no volatility and is 0 risk for the long term investor. I am saying that bond does in fact carry risk and contains volatility. I think that is the disagreement we are having.


All else being equal, I generally defer to the maxims that risk and return are linked and there is no free lunch in investing except diversification. I accept 100% equity portfolios will beat 60/40 portfolios over long periods of time the vast, vast majority of the time. This is because they are riskier. There is a lot of consensus on this side of the argument. Volatility in the short term (over months, years, decades, etc.) SHOULD matter in my opinion, even to the long term investor with the 30 year horizon. You disagree and that's fine, but I think it would be a good idea in the future for you to pre-define how you are using the terms "risk" and "volatility" because you are assigning meanings to those terms that are contrary to the commonly accepted meanings.
First, I don't think I wrote anything about the volatility of nominal returns. So I disagree that I said this:

"You are saying that bond has no volatility and is 0 risk for the long term investor."

Second, I tried to be very clear that I was referring to the standard deviation of the historical population of 20 and 30 year real returns of U.S. equities and U.S. bonds. Perhaps I should review my previous comments to be sure.

With respect to whether my meanings of risk and volatility are contrary to commonly accepted meanings: although many investment journalists only refer to the volatility of annual or monthly returns, many academic researchers have compared the Standard deviations and Sharpe ratios of investments over varying holding periods. Almost every study I've seen which considers 1 year vs 5 year vs 20 and 30 year holding periods points out that equities become less volatile than bonds when the holding period is 20 years or more.

Here's a passage from Professor Jerrmy Siegel's widely read book, "Stocks for the Long Run":

"Standard deviation is the measure of risk used in portfolio theory and asset allocation models. Although the standard deviation of stock returns is higher than for bond returns over short term holding periods, once the holding period increases to between 15 and 20 years, stocks become less risky than bonds. Over 30-year periods, the standard deviation of equities falls to less than three-fourths that of bonds or bills. The standard deviation of average stock returns falls nearly twice as fast as for fixed-income assets as the holding period increases."

You may not agree that the standard deviation of rolling 20 or 30 year returns is an appropriate measure of risk. I see it this way: the standard deviation, or volatility, of assets based on weekly returns would not be appropriate for investors with a three-year horizon. Weekly variations would be noise that should be ignored. For investors who plan to buy and hold for 30 years, annual variances of asset returns are likewise noise which should be ignored.

I recognize that many investors do not have the tolerance for short term risk that I have. Where we probably disagree is that I believe such risk aversion is the result of advisors and mass media constantly pounding in their heads that stocks are risky. I suppose I should be happy that the majority of investors are so averse to very short term fluctuations, as I have been able to enjoy much higher returns than I otherwise would with my aggressive equity portfolio.

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Re: The Mathematics of Retirement Investing

Post by jbolden1517 » Thu Aug 17, 2017 2:24 pm

longinvest wrote:
Wed Aug 16, 2017 1:57 pm
Other investors will consider that it is a reasonable cost to pay to lower the volatility of their portfolio and reduce the risk of failure of their retirement plan.
Of course in the real world for a person with a small portfolio and a large income stream coming into the portfolio volatility is helpful not harmful to returns. Decreasing volatility decreases not increases returns for young investors. That ceases to be true quite quickly but we are discussing the young.

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Re: The Mathematics of Retirement Investing

Post by jbolden1517 » Thu Aug 17, 2017 2:40 pm

bigred77 wrote:
Wed Aug 16, 2017 8:40 pm
Bonds have beaten equities over 30 years on occasion. We all admit it's an extremely unlikely event to occur, but it's absolutely possible.
I think you meant 20 year periods where it has happened 3% of the time. It has happened 0% of the time for 30 year periods. That's holding with no leverage. Most of the safe bonds that Bogleheads talk about are designed to be held on some form of leverage to produce an adequate return. When we are talking about young investors in a retirement account they can't directly leverage. If bonds are going to outperform the best way to do this is hold financial stocks (or CEFs) that represent leveraged bonds.

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Re: The Mathematics of Retirement Investing

Post by itstoomuch » Thu Aug 17, 2017 2:58 pm

If many Boomers are like wife and I, they will most of their retirement funds in IRAs, and will ultimately face RMD, not Safe Withdrawal rates. The rare retiree will take excess RMD, above their SWR, and invest/save in taxable accounts.
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Re: The Mathematics of Retirement Investing

Post by willthrill81 » Thu Aug 17, 2017 2:59 pm

jbolden1517 wrote:
Thu Aug 17, 2017 2:40 pm
bigred77 wrote:
Wed Aug 16, 2017 8:40 pm
Bonds have beaten equities over 30 years on occasion. We all admit it's an extremely unlikely event to occur, but it's absolutely possible.
I think you meant 20 year periods where it has happened 3% of the time. It has happened 0% of the time for 30 year periods.
No, it's happened twice. There was a period beginning in the 1800s as I recall where long bonds beat equities. Also, the other period began around 1982, and 30 year bonds (with rate over 11%) just squeezed out 30 year equity returns. Still, twice in around 200 years of history does not even qualify as a bet.

Not long ago, I heard a fellow talking about how scared people were in the early 1980s to buy long-term CDs paying 16% because they were (justifiably IMO) concerned about inflation. There isn't nearly as much certainty with bonds and FI as many think there is.
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Re: The Mathematics of Retirement Investing

Post by willthrill81 » Thu Aug 17, 2017 3:02 pm

itstoomuch wrote:
Thu Aug 17, 2017 2:58 pm
If many Boomers are like wife and I, they will most of their retirement funds in IRAs, and will ultimately face RMD, not Safe Withdrawal rates. The rare retiree will take excess RMD, above their SWR, and invest/save in taxable accounts.
It's been shown by Wade Pfau and others that spending all of one's RMDs, assuming a balanced portfolio, is actually a very conservative strategy.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: The Mathematics of Retirement Investing

Post by bigred77 » Thu Aug 17, 2017 3:04 pm

jbolden1517 wrote:
Thu Aug 17, 2017 2:40 pm
bigred77 wrote:
Wed Aug 16, 2017 8:40 pm
Bonds have beaten equities over 30 years on occasion. We all admit it's an extremely unlikely event to occur, but it's absolutely possible.
I think you meant 20 year periods where it has happened 3% of the time. It has happened 0% of the time for 30 year periods. That's holding with no leverage. Most of the safe bonds that Bogleheads talk about are designed to be held on some form of leverage to produce an adequate return. When we are talking about young investors in a retirement account they can't directly leverage. If bonds are going to outperform the best way to do this is hold financial stocks (or CEFs) that represent leveraged bonds.
No I was referring to a 30 yr holding period. By "stocks" I really meant "only the S&P500" and by "bonds" I meant "Long-Term Government Bonds". I think it was for a very specific 30 yr period ending around 2010. There was a big hoopla in the media about it.


Edit... I see will beat me to it...I did find this article from back then. https://www.cbsnews.com/news/bonds-beat ... s-so-what/

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Re: The Mathematics of Retirement Investing

Post by bigred77 » Thu Aug 17, 2017 3:14 pm

jbolden1517 wrote:
Thu Aug 17, 2017 2:40 pm

I think you meant 20 year periods where it has happened 3% of the time. It has happened 0% of the time for 30 year periods. That's holding with no leverage. Most of the safe bonds that Bogleheads talk about are designed to be held on some form of leverage to produce an adequate return. When we are talking about young investors in a retirement account they can't directly leverage. If bonds are going to outperform the best way to do this is hold financial stocks (or CEFs) that represent leveraged bonds.
Also wanted to add... C'mon now,,, that bolded part is pretty ridiculous.

Bogleheads talk about holding intermediate term bonds, mostly issued by the US Government. Intermediate term treasuries are in no way "designed to be held on some form of leverage to produce an adequate return". They are designed to raise capital for the government and are auctioned off to investors at market rates. They are recommended by most on this board as a safe asset and the best way dampen portfolio volatility. And by volatility, just to avoid any confusion, I mean to lessen the way equity heavy portfolios can rise and fall dramatically in value over shorter periods of time : days, months, couple years, etc. :mrgreen: (Not a shot at you North Texas Cajun) :mrgreen:

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Re: The Mathematics of Retirement Investing

Post by jbolden1517 » Thu Aug 17, 2017 3:38 pm

willthrill81 wrote:
Thu Aug 17, 2017 2:59 pm
No, it's happened twice. There was a period beginning in the 1800s as I recall where long bonds beat equities. Also, the other period began around 1982, and 30 year bonds (with rate over 11%) just squeezed out 30 year equity returns. Still, twice in around 200 years of history does not even qualify as a bet.
Sure I know zeros have done well. I was using "bonds" in the Boglehead sense to mean intermediate bond funds. Lots of bonds beat a total market portfolio once you go outside those realms. Heck a long credit default swap in 2007 paid something like 1000:1. Try and get that from stocks. 1800s example I don't know about, makes sense though. There were some pretty big spikes in bond rates then.
willthrill81 wrote:
Thu Aug 17, 2017 2:59 pm
Not long ago, I heard a fellow talking about how scared people were in the early 1980s to buy long-term CDs paying 16% because they were (justifiably IMO) concerned about inflation. There isn't nearly as much certainty with bonds and FI as many think there is.
The government for a short period of time tried bearer bonds to get debt to sell at reasonable interest. The bottoms of bear markets are pretty wild. That's why I like going after bears and investing in them.

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Re: The Mathematics of Retirement Investing

Post by jbolden1517 » Thu Aug 17, 2017 3:41 pm

bigred77 wrote:
Thu Aug 17, 2017 3:14 pm
jbolden1517 wrote:
Thu Aug 17, 2017 2:40 pm

I think you meant 20 year periods where it has happened 3% of the time. It has happened 0% of the time for 30 year periods. That's holding with no leverage. Most of the safe bonds that Bogleheads talk about are designed to be held on some form of leverage to produce an adequate return. When we are talking about young investors in a retirement account they can't directly leverage. If bonds are going to outperform the best way to do this is hold financial stocks (or CEFs) that represent leveraged bonds.
Also wanted to add... C'mon now,,, that bolded part is pretty ridiculous.

Bogleheads talk about holding intermediate term bonds, mostly issued by the US Government. Intermediate term treasuries are in no way "designed to be held on some form of leverage to produce an adequate return". They are designed to raise capital for the government and are auctioned off to investors at market rates. They are recommended by most on this board as a safe asset and the best way dampen portfolio volatility. And by volatility, just to avoid any confusion, I mean to lessen the way equity heavy portfolios can rise and fall dramatically in value over shorter periods of time : days, months, couple years, etc. :mrgreen: (Not a shot at you North Texas Cajun) :mrgreen:
I agree they are auctioned off at market rates. Generally to be held by banks or other financials who are on leverage. I also agree they dampen portfolio volatility. They are mostly cash, with a little duration risk thrown in. The cash is a waste for a young investor, the duration risk is a nice diversifier. Leverage gets rid of the cash problem.

Or another way to think of it is this. The leverage is what connects short term rates and long term rates.

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Re: The Mathematics of Retirement Investing

Post by AtlasShrugged? » Sat Feb 10, 2018 11:58 am

longinvest, #Cruncher....Quick question. Will the spreadsheets be updated for the new tax rates?
“If you don't know, the thing to do is not to get scared, but to learn.”

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Re: The Mathematics of Retirement Investing

Post by longinvest » Mon Feb 12, 2018 11:53 am

JCE66,
#Cruncher wrote:
JCE66 wrote:
Sat Feb 10, 2018 11:58 am
longinvest, #Cruncher....Quick question. Will the spreadsheets be updated for the new tax rates?
I don't stay informed about US tax rates changes. Maybe #Cruncher does and would be willing to provide a new version of his nice little spreadsheet.
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Re: The Mathematics of Retirement Investing

Post by #Cruncher » Mon Feb 12, 2018 2:38 pm

JCE66 wrote:
Sat Feb 10, 2018 11:58 am
... #Cruncher....Quick question. Will the spreadsheets be updated for the new tax rates?
Here is the updated method for creating the 2-column spreadsheet discussed in this post:

Select all, copy, and paste at cell A1: [*]

Code: Select all

Years
Withdrawal rate
Salary
Social Security
Adjust working spending $ for retirement
Retirement % of adjusted working spending
Base tax
Plus marginal tax rate of
On excess over
Growth rate
$1 grows to
="Withdrawal @ "&TEXT(B2,"#0%")
Needed savings per year
Salary less savings
Tax
Salary less savings less tax
="After "&B1&" years savings grow to"
="Withdrawal @ "&TEXT(B2,"#0%")
Plus Social Security
Tax
Withdrawal plus Social Security less tax
Retirement $ versus working
Retirement percent of working
Select all, copy, and paste at cell B1: [*]

Code: Select all

30
0.04
80000
25000
-10000
1
=10%*9525+12%*(38700-9525)
0.22
=38700+12000
0.069
=FV(B10,$B1,-1,0,0)
=$B2*B11
=($B6*($B3+$B5-$B7-$B8*($B3-$B9))-$B4+$B7+$B8*($B4-$B9))/(B12-$B8*B12+$B6*(1-$B8))
=$B3-B13
=$B7+$B8*(B14-$B9)
=B14-B15
=FV(B10,$B1,-B13,0,0)
=$B2*B17
=$B4+B18
=$B7+$B8*(B19-$B9)
=B19-B20
=B21-B16
=B21/B16
The only changes are two formulas and one constant in cells B7:B9:

Code: Select all

              2017                         2018
     --------------------------   --------------------------
B7:  =10%*9325+15%*(37950-9325)   =10%*9525+12%*(38700-9525)
B8:  0.25                         0.22
B9:  =37950+10400                 =38700+12000
This will change the tax in cell B15 from $10,928 to $8,930.

* With some Excel versions you'll need to choose Paste Special and Text.

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AtlasShrugged?
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Re: The Mathematics of Retirement Investing

Post by AtlasShrugged? » Wed Feb 14, 2018 5:22 am

Here is the updated method for creating the 2-column spreadsheet....
#Cruncher....You are awesome!
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