Category Archives: Risk Management

The Arithmetic of Prudence, Part 3

Part 2 of this series dealt with the asymmetry of marginal utility and that prudence often requires maximizing the probability of reaching a minimum objective rather than maximizing the expected portfolio value. This is especially true when one or more of the following applies:

  • The time horizon is short, e.g. < 10 years.
  • The investor is a prodigious saver; i.e., less reliant on returns to reach goals.
  • The portfolio is in distribution.

The table below summarizes my portfolio recommendation depending on the life stage of the investor.

The demarcation between early and late accumulation, early and late distribution are 10 years to and from the retirement date, respectively. Other authors have referred to the decade before and after retirement as the retirement red zone. Michael Kites recommends a “bond tent” from 10 years before to 15 years after retirement. It has a more elongated taper but based on the same principles.

The recommendation is for principles only. There isn’t specific allocation recommendation due to the enormous variation in individual risk tolerances. 70% stocks/30% bonds may be ultra conservative to one and a roller-coaster ride to another. However, the relative measures of risk ought to hold for the same investor at different stages of his investing life. I also believe in the soundness of some popular advices: greater allocation to equities during early accumulation and the use of annuities (SPIAs) for baseline income during late distribution.

As laid out in Part 2 of this series I advocate sacrificing some growth for reduced volatility in late accumulation and early distribution. The need to do so is recognized by mainstream writers but I find their typical advice of increasing the fixed income allocation too simplistic. I have written about the alternative asset classes in Beyond 60/40. In my own portfolio I continue to explore cost-effective ways to incorporate these assets consistent with modern portfolio construction methods such as risk parity, minimum correlation and maximum diversification but tailored to an individual investor with a desire to reduce trading frequency.

We live in an age where competition in the financial services industry has given the individual investor access to an unprecedented array of products at reasonable costs. Of course, not all of them make sense and the onus is upon us to separate the wheat from the chaff. But quite often I see in the PF blogosphere and forums an avoidance on principle. In some there is a suspicion to all things from the financial services industry, a suspicion no doubt born out of experience with its dodgy business practices. In others, it feels like a fundamentalist fervor against anything not a 3-fund portfolio. Whatever the reason, the majority of the DIYers continue clinging to 60-year old portfolio construction methods. I have never tried to convert anybody but have always read forum (e.g. Bogleheads) exchanges about alternative assets (typically gold) and portfolio construction (slice-and-dice, factors) with interest — when emotions are high and arguments are well-thought it makes a great spectator sport!

In the table I had the same recommendation for both late accumulation and early distribution. For obvious reasons my mental efforts have been directed to late accumulation. After the retirement threshold I can see greater emphasis on income generation: increasing allocation to CEFs, higher yielding stocks, more aggressive option writing, and less emphasis on speculative assets. The asset categories will remain the same but the percentage will differ. I expect tax considerations to play a larger role than return-volatility trade-offs.

Speaking of the distribution phase, two recent opus (both are deserving of this word) contributed significantly to our understanding: a series by EarlyRetirementNow and the work by none other than the great Bill Sharpe. Bill Sharpe also called decumulation “the nastiest, hardest problem in Finance”. It is indeed difficult, if not insoluble, if the requirements are:

  • The only allowed assets are equities and bonds.
  • The allocation is static or follow a simple age-dependent formula.
  • The withdrawal rate is anywhere close to 4%.

As they say, 2 out of 3 ain’t bad. Variable withdrawal strategies can help, but critics will say they’re market-timing in disguise: in effect, if not on purpose. PortfolioCharts has repeatedly shown the benefits of gold in increasing the safe and perpetual withdrawal rates, but gold haters will continue to hate. I suppose that leaves getting more money/requiring less as the fool-proof way of ensuring success. But try to tell that to a 23-yr old ER-aspirant!

So far as my own plan is concerned, none of the three bullets apply. But since I’m far from the Epicurean ideal, I’ll be working for another 10-12 years yet!

Decision Time

This is another market commentary following my post on March 23rd, A Correction May Be Upon Us; and 29th, Lightly Held Opinions. The prediction was a drop then bounce in April, then a deeper drop in May that could potentially last into July. The bounce in April was flagged to have the potential to make a new high in the 2nd post. So what has happened so far?

The chart is of the S&P where the low of 2322 was reached on the 27th. There was a retest of the low on Apr 13th as concerns with North Korea reached a fevered pitch. The bounce up to 2398 was just shy of the 2400 peak on March 1st. The other indices behaved slightly differently: the DOW made a lower low whereas both Nasdaq and Russell 2000 made new highs on the bounce. Overall, I’d say things played out as predicted. The bigger question is, will the deeper correction come?

I’m leaning towards “yes” on that one, although I would temper the probability for the most severe scenarios — retesting of the election or even the Brexit lows. If you take a look at the Fibonacci levels in the first post, 2280 would be the first target, the breaking of which will put into question the 2240 level which is also the current 200 DMA. I would expect the next support at 2200 to hold in most cases. In terms of near term catalysts there is plenty: the FOMC meeting, April employment report and the French election all within a week’s time, not to mention North Korea. That said I always view external events as excuses for releasing the internal pressure: in this case there being too many people along for the ride, and the market never makes it easy for everyone to make money.

What I’ve done in the mean time

I added to a couple names on weakness. I sold puts on Apr 13th when there was well over 1% premium on 2-week OTM puts. They have expired worthless. I also sold some covered calls and 1 stock in the last two days. Not a whole lot different if I was just DCA in the absence of any directional views. The biggest portfolio change was deciding to trim my emergency fund allocation. I sold a CD and moved that money to the active accounts such that its cash position is now 14%.

What if I’m wrong and the market goes straight up from here?

First of all, I don’t see a bear market developing, and if that’s your view you should examine your information sources and your logic. If the correction doesn’t come, I’ll continue to DCA into the names I already picked out. Fortunately we should know the answer soon. One thing is for sure: I’ll not leave cash on the sidelines when this bull market takes off.

So why pay so much attention to this particular intermediate low when my stated approach to market timing is to avoid the real nasty bear markets and hold through the shorter gyrations? First, to constantly validate our hypothesis against the market is how we learn and improve. Second, there are leveraged bets that require a margin of safety that comes when “there’s blood on the street”. The flip side to avoiding the bear market is to fully take advantage of the bull market, both require accurate reading of the situation.

A Correction May Be Upon Us

The long waited correction may be finally upon us. The 1%+ drop in the S&P on Mar 21st was the first in over 100 days. The bounce on the 22nd was anemic and accompanied by low volume. Most of today (23rd) was spent in positive territory but sellers took over in the last two hours — a very tell-tale sign. As in the chart below, we have broken below the trend line from the November election. Given this evidence, I’m of the opinion that an intermediate correction of months in duration has started.

I’ll go out on a limb again in trying to forecast a duration and depth of this correction. My model is signaling a bounce in April and a resumption of decline in May with a hard drop and bottom into July. I have little confidence in the exact path but a correction of 4+ months in duration will match that of the rise, a symmetry that would be appealing. The Fibonacci levels for this “Trump rally” aligns nicely with regions of minor support/resistance. I don’t trade at those time intervals but it’s interesting nonetheless. Given the nature of the in-flows of this rally, and that the market is never kind to Johnny-came-latelies, there is a high probability we’ll retrace all the way to the November bottom and more. I would go so far as saying that the “Brexit” bottom of 1991.68 is also in play.

Why do I bother with this kind of predictions and what do I plan to do with that information anyway? First and foremost it’s to develop a feel for the market and secondly to build confidence in the model. I’ve been clear on my approach to market-timing. My main goal is to be able to avoid the “big one” and ensure that my family is provided for. The skills that I’m honing are essential in deciphering the macro trends.

Since the inception of this blog, my most significant market timing move, in terms of duration and amount of capital, was the avoidance of nominal bonds. 35-40% of my passive portfolio has been in stable value funds paying 2 or 3% per annum. It’s been a good move — AGG has lost 3% since Aug’16. Compared with that that my pruning of stocks is rather opportunistic. In full disclosure, my pace of selling picked up in Feb/Mar, but it was not due to my market view. The main reason was the rotation in my fixed income allocation precipitated a desire to limit dividend payouts. This morning I closed out the MCD/DIS option spreads mentioned in this post, along with a couple other positions to give me a 12.7% cash position in my active portfolio. I don’t have plans for more sales; instead there are 7-9 buy candidates. My longer term view remains that we are in a full-blown bull market; but first, we’ll have to wait out this correction.

Closed End Funds

My current asset allocation has about 35% in fixed income/cash, which is about age – 10. Within the passive portion, 40% is fixed income (FI), split between stable value (SV) funds and the total bond market (TBM) 35/5. The interest rate is about 2% for the SV funds in my 401K and an outstanding 3+% in my wife’s 401K. They compare favorable to current bond yields such that I’m considering getting out of TBM altogether. Views on my approach to FI in my passive accounts may vary from mainstream to conservative.

The opposite is true in my active accounts where I use leveraged closed end funds (CEFs) for the FI allocation. In open-end mutual funds, investors transact with the mutual fund company. In closed-end funds, investors buy or sell fund shares with other investors on an exchange. CEFs operate just like an ETF except usually they’re actively managed. ETFs have a fund sponsor who can create/destroy fund units in response to demand so that fund price tracks closely its net asset value (NAV). In contrast, CEFs can have market values that deviate substantially from NAV. Such discount/premium is a key evaluation criterion for CEFs.

One outstanding feature of many CEFs is their high current yield. For example, I own PCI, PDI and PTY in my tax-advantaged accounts. PCI/PDI are multi-sector funds, whereas PTY is a corporate bond fund. All are managed by Pimco. Yields in the trailing 12 months were 12-14%. Double digit yields were made possible by employing leverage, typically around 40% (achieved by issuing lower-yielding preferred shares). Leverage works both ways so you can say my overall approach to FI is a “bar-bell” in terms of risk. CEF management fees are on par with (the more expensive) active mutual funds but obviously the after-fees return is the primary consideration. Pimco funds are known to employ derivatives to hedge interest rate risk which makes them particularly valuable in this environment.

In my taxable account, I also own leveraged muni CEFs, PCQ and PCK, both CA muni funds managed by Pimco (yes I think they are the best in this business). They’re yielding 5.5-6% which is close to double digit pre-tax yields depending on your tax bracket. They dropped quite a bit post election since certain anticipated tax changes will make them less attractive. I’m less worried about these tax changes than the longer term fiscal situation in California. For now they are medium term (~2 years) holds. I will not add to them, but rather will seek opportunities to sell especially if I can create more space in my tax-advantaged accounts.

The backdrop of any FI discussion is of course the direction of interest rates. I believe rates have in fact bottomed. Not all is lost for FI though. Hedging with interest rate derivatives is one approach. For now, MBS (mortgage backed securities) should do quite well as pre-payments stop. Floating rate loans should do quite well, too. In fact, I’ve already picked out a CEF in the latter category for my watch list.

There is far more diversity in FI as I pointed out in Beyond 60/40. A recent post from Newfound Research did an excellent job decomposing risk factors in various FI instruments:

Most individual investors have an FI allocation heavy in treasuries and investment grade corporates which is a lot of rate exposure (see LQD and TLT in the graph). I find it ill-advised giving my outlook on rates. At any rate, individual investors tend not to pay much attention to FI, since they tend to be overweighted in equities anyway. Readers of this blog though should not be surprised by where I stand. I don’t think a TBM index fund works nearly as well as its equity counterpart. One reason being the index is weighted by issuance. That there are non-economic, state actors with heavy footprints is another. Not to mention it doesn’t cover SV funds, CDs, and bank loans if one considers all the FI options available.

Supplementing DGI for Retirement Income

A common criticism for DGI for retirement income is that it requires a higher portfolio value due to current low yields, thus over-saving and longer working years. That is a valid point. The canonical approach for retirement income generation is to withdraw a fixed percentage, e.g. 4% from a $1M portfolio for an initial annual income of $40K. The S&P 500 yields just over 2% today. A 4% yielding portfolio will force one into high yielding but low growth sectors such as utilities, telecoms, and REITs, etc. This naturally increases portfolio risk.

My solution is: supplementing a well-rounded, high quality DGI portfolio with high-yielding CEFs. Let’s do some quick math. Assuming the DGI portfolio yields 2.5% and has a 7% annual growth rate. We can also construct a CEF portfolio with 8% yield and assume no principle growth. Then the combination of $727K in the DGI portfolio and $273K in CEFs will generate $40K initially. The weighted portfolio growth will be 0.727 x 7% > 5%, more than enough to overcome inflation. All of the assumed numbers are quite conservative and can easily be constructed from securities available today.

Readers interested in investing in CEFs should do their due diligence. Two resources I find tremendously helpful are CEFConnect and the MorningStar discussion forum.

The Arithmetic of Prudence, Part 2

In the second installment of this series I want to further expound on the point made at the end of Part 1: that when projecting into the future, the expected value is the mean which for a normal distribution is the same as the median or the 50 percentile value. A more comprehensive approach is to examine the distribution of all possible outcomes. Keeping in mind the asymmetry between the extra pain from missing the target number and the more subdued joy from exceeding it, a prudent planner may want to optimize a lower percentile outcome, e.g. 10 or 25 percentile.

To illustrate the point I present the probability density functions (PDFs) of the ending values of two hypothetical portfolios . For simplicity, the outcomes are assumed to follow standard Gaussian distributions [the actual parameters are mean = 115 and standard deviation (SD) = 20 for Portfolio 1, mean = 100 and SD = 5 for Portfolio 2]. The target portfolio value is indicated by the red dash line. I intentionally left out the context where for this exercise to make it as general as possible. It could be about reaching the number at the end of accumulation phase to support a certain retirement lifestyle; or it could be about the end of the distribution phase where success means portfolio value is positive.

The majority outcome from both portfolios are to the right of the red dash line: both portfolios are likely to meet the financial goals, a very good thing. Now let’s delve a little deeper. The expected ending values are at the center of the respective distributions and clearly Portfolio 1 has a higher value. On the other hand, Portfolio 1 has a wider spread or larger standard deviation. Note that the areas below the two curves both equals 1 by definition. The areas under the curves to the left of the red dash line represent the probability of failure. Portfolio 1, despite having a higher expected value, actually has a higher probability of failure! As you can see from the diagram, the two PDFs cross at some point, the exact location depends on the relative mean and SDs. Mathematically, when we examine the left side of the distribution we’re looking at lower percentile outcomes. For example, in calculating withdrawal scenarios we regularly look at the 95% confidence level, in other words, the 5 percentile outcome. It is my contention that a more conservative planner should pay more attention to the lower percentile outcomes (the “sure thing”) than the mean expected value.

While it is often the case that a portfolio with higher expected rated of return will also have a larger standard deviation, the two PDFs above were specifically chosen to illustrate a point. We should rightly ask how real portfolios behave. To that end, we can turn to the excellent tools available at

Step 1. Determine sample portfolio CAGR and SD from backtesting

First we establish three sample portfolios: portfolio 1, 100% equities with a 50/50 US/international split; portfolio 2, a 60/40 3-fund portfolio, again with a 50/50 US/international split in equities, and the total bond market for the fixed income portion; and lastly the Permanent portfolio with equal weights in US equities, long and short term treasuries, and gold. Note that the backtest was from 1987, the earliest time data on all asset classes involved was available. The CAGRs were 7.79%, 7.53% and 7.11% respectively. The SDs were 15.53%, 9.35% and 7.11% respectively. There was a clear reduction in volatility from adding bonds, while the Permanent Portfolio exhibited even less volatility as expected. The difference in CAGR appeared minor but would be appreciable over a multi-decade compounding period. My personal view in portfolio construction is that the closer to the end of the projection period the greater impact of volatility and lesser of CAGR.

Step 2. Use Monte Carlo simulation to project portfolio value at the end of distribution phase

For illustration purposes I’ll use Porfoliovisualizer’s Monte Carlo simulation tool for a standard 30-year withdrawal at 4% of portfolio value per year, matching the recommendations from the famous Trinity study. The starting portfolio value is $1MM, the parameters of the Monte Carlo study was set up as follows: statistical returns from 1987-2015 was used (only slightly different from the numbers from 1987-2016), assume returns follow normal distributions, and a 3% inflation with a volatility of 1.5%.

The screen capture above shows the simulation the 100% equity portfolio. Results are for 25/50/75 percentile ending portfolio values. The same simulations were run for the 60/40 3-fund portfolio and the Permanent portfolio and summarized below.

For both the 50 and 75 percentile results, the 100% equity portfolio has by far the highest expected value, followed by the 60/40 portfolio and then the permanent portfolio. However, when looking at the 25 percentile results, the order is exactly reversed with the Permanent Portfolio on top and the 100% equity portfolio on the bottom. Here we have a situation similar to the very first, entirely hypothetical diagram: the portfolio with lower expected value but tighter spread wins when examining lower percentile outcomes. So the take-away is that for conservative planners who want to adopt a maximin approach (maximize the guaranteed minimum) looking at the expected value alone can give misleading results.

A couple footnotes to the study above: 1) the start date of 1987 missed one of the biggest bull markets in gold so should have hurt the Permanent Portfolio, 2) in the Monte Carlo simulations, normal (Gaussian) return distributions was assumed instead of fat-tailed distributions which probably helped equity-rich portfolios, 3) my assumption of 3% inflation was based on current economic conditions and didn’t seem to make a big impact on the results, 4) note the study is NOT a forecast, backtesting was used to establish historically realistic CAGRs and SDs which under a standard withdrawal plan provided historically realistic portfolio value probability distributions. These probability distributions proved that the PDFs shown in the first diagram were qualitatively correct.

Edit: added the assumption that the distribution is normal, thus the mean and median are the same.