Effective Equity

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EFFECTIVE EQUITY. How do you assess portfolio VOLATILITY? Unfortunately, there are very few FREE tools available to do this. One way is to calculate EFFECTIVE EQUITY, or RELATIVE SD [SD = standard deviation], of the portfolio that has mixed type of assets [stocks, bonds, alternatives]. Currently, PORTFOLIO VISUALIZER. com [search] provides portfolio standard deviation [SD] for free; this can/does change as free websites eventually want to monetize [years ago, I used a website that was acquired by MSCI and that data are now available for pay only]. Use PV “Backtest Portfolio” feature to find the ratio of SD_portfolio and SD_sp500 [or, another benchmark]. If the result is, say, 0.65, then the portfolio has 65% of the volatility of SP500, or 65% effective equity. Surprisingly, effective equity can be 5-15% higher than nominal equity that people use otherwise. This is because different stocks have different levels of volatility, and bonds and alternatives also contribute to portfolio volatility due to their CORRELATIONS with equity. A future post will explain how to use this for PORTFOLIO ALLOCATION. #AssetAllocation , #PersonalFinance . Posted 11/19/20 AM

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Theory behind effective-equity.

Standard deviation [SD] is an absolute measure of volatility, i.e. it is independent of benchmark. It can be used for different asset classes, so it is useful for evaluating portfolios with mix of stocks, bonds, mutual funds [OEFs], ETFs, CEFs. Bonds have rate and credit risks and the latter is correlated with stocks.

Effective-equity is defined as Relative_SD [= SD/SD_benchmark]. It is dimensionless and is related to beta [short-term volatility] and correlation coefficient r as,

Effective-equity = Relative_SD = beta/r

Effective-equity can be stated as fraction or %.

The above result can be seen easily by writing out the expressions for SD, beta and r.

Effective-equity depends on the benchmark used [e.g. SP500], as do beta and r. Its value is quite stable, so one can use either 3 or 5 years to capture different market conditions.

M* Quote page/Risk data are updated monthly for SD [and other statistics] and can be used for effective-equity.

For funds [and stocks], M* Portfolio "My View/Customize My View" has 3-yr SD that can be added to one of "My Views". Frequency of update is not clear but should also be monthly; it can be verified by comparing SD of SP500 or VFINX in Quote page and M* Portfolio. Note that the SD entry for the portfolio is blank because the portfolio SD is a complex calculation due to cross-correlations [it is not the weighted average of SD; that overestimates portfolio SD (with the assumption of all cross-correlations as 1.0)]. A long hand way to calculate portfolio SD would be to generate a table of portfolio values, calculate daily or weekly or monthly returns, and from that portfolio SD [and other statistics] can be calculated. Luckily, PV provides portfolio SD based on monthly returns.

Portfolio Visualizer [PV] month-to-month run data is up to date as of the most recent full month and it can be used to determine effective-equity for stocks, funds and portfolios over various timeframes [1, 3, 5, yrs]. Unfortunately, the PV [or M*] SD data are based on monthly returns that don't capture intra-month volatility. In a way, the monthly data smooths daily or weekly data. It would be be better to use SD based on daily or weekly returns but there is no free source for that.

It is not a good idea to mix SD from different sources, so all SD data should be from a single source [PV or M* or another]. The math should be same but some sites use monthly returns vs excess monthly returns [returns in excess of risk-free returns (typically, 3-mo T-Bills)] and that may cause issues. Updating frequency and mismatch of dates are other issues.

The formula above can be rewritten as,

SD = (beta/r) x SD_benchmark

Note that all terms on the right hand side are benchmark dependent, but that effect cancels out as SD on the left hand side is independent of benchmark.

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Example - Allocation/Balanced funds VWELX, JABAX, DODBX

LINK PV Run 3 Yrs, 3/1/18-2/28/21

In the Portfolio Visualizer run with month-to-month option, the start-month is from the 1st and the end-month is to the last day. Note the dates for 3 years, March 2018 - February 2021, 3/1/18-2/28/21.                

                    SD          Relative_SD         Effective-Equity          Derived Classification            M* Classification

VWELX       11.64         0.6306                  63.06%                   Moderate-Allocation         Allocation 50-70% Equity
JABAX        11.23         0.6083                  60.83%                   Moderate-Allocation         Allocation 50-70% Equity
DODBX       16.20         0.8776                  87.76%                   Aggressive-Allocation       Allocation 50-70% Equity
SP500        18.46         1.0000                  100.00%                        Reference                      Large-cap Blend                                  

So, VWELX and JABAX are well within the framework of moderate-allocation, but DODBX is positioned as aggressive-allocation, in spite of their M* classifications based on their nominal-equity. It is often said that DODBX is among the most aggressive of moderate-allocation funds, but the data above show that it is really acting as aggressive allocation once the nature of its stocks and bonds are taken into account.


M* Definitions                         Common Terminology

Allocation 15-30% Equity         Conservative-Allocation [CA1]
Allocation 30-50% Equity         Conservative-Allocation [CA2]
Allocation 50-70% Equity         Moderate-Allocation [MA]
Allocation 70-90% Equity         Aggressive-Allocation [AA]

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Another Example - 50% VFIAX [SP500], 50% VUSTX [Long Treasuries]

PV Run 3 Yrs 3/1/18-2/28/21

Effective-equity for the Mix 47.35% [conservative-allocation/CA2], VFIAX 100%, VUSTX 70.31% [note the negative correlation below]

Correlations r for the Mix +0.72, VFIAX +1.00, VUSTX -0.36

So long as there is +/- correlation, effective-equity accounts for it. But it may be confused when somethings in the portfolio are not correlated to SP500 [benchmark]. Also, somethings may move out of phase.

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In a new article on risk, M* has some good info on standard deviation (SD). Rolling 3-yr month-to-month SDs show that SD is not static. However, as it is used for effective-equity here, all SDs adjust and lot of variability (but not all) is removed from Relative-SD or effective-equity.
www.morningstar.com/articles/1091929/hello-risk-our-old-friend

Image link im.morningstar.com/content/CMSImages/20802.png

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See also the Twitter link,

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MPRS - M* Portfolio Risk Score, 4/30/22-
www.morningstar.com/articles/1095429/morningstars-allocation-categories-get-an-upgrade

M* finally took an important step in assessing total risk of hybrid portfolios (allocation/balanced, multi-asset) that takes into account any additional risks by the stock and bond portions. It has developed M* Portfolio Risk Score (MPRS) that is correlated with period-relative-beta (unlike Effective-Equity that uses period-relative-SD). A broadly diversified stock portfolio like SP500 may have MPRS around 100. As an example, if a fund with nominal equity in 30-50% range has MPRS of 65, its placement will be in the 50-70% range (MMTR). In any event, this new M* way of classifying allocation/balanced and multi-asset funds should remove some of the M* misclassifications of some funds that YBB has pointed out for years by using the Effective Equity measure (described earlier in this thread). It will be a huge improvement over the old M* allocation/balanced fund classifications that were based simply on nominal equity percentages. It is unclear whether the MPRS values will be indicated on the fund pages at the M* website (they are not on 5/28/22).

M* has also gone back to using descriptive terms for allocation/balanced and multi-asset funds with some added refinements.

Percent-Based Names                Descriptive Names

Allocation - 15%-30% Equity         M* Conservative Target Risk (MCTR)

Allocation - 30%-50% Equity         M* Moderate Conservative Target Risk (MMCTR)

Allocation - 50%-70% Equity         M* Moderate Target Risk (MMTR)

Allocation - 70%-85% Equity         M* Moderate Aggressive Target Risk (MMATR)

Allocation - 85%+ Equity               M* Aggressive Target Risk (MATR)

On May 28, 2022, for the affected funds (FKIQX, OAKBX, etc), M* is still showing their old classifications on the Quote tabs, their new classifications as of 5/27/22 on the Performance tabs and their new classifications as of 4/30/22 on the Risk and Portfolio tabs. Presumably all will be fixed up in the next monthly updates of fund pages in early-June. 

Example - FKIQX

Nominal Equity 38.59%, New MPRS 68.81 (M* article by JK), Effective Equity 63.67% (from PV run)

Old M* classification: Allocation - 30%-50% equity

New M* classification: Allocation - 50%-70% equity (MMTR)

Classification by Effective Equity: Allocation - 50%-70% equity (MMTR)


The new M* Fund Category Definitions may also show some related details or explanations. This document is typically issued/effective in April, but is not published as of 5/28/22. When it becomes available, it will be posted on this thread,
ybbpersonalfinance.proboards.com/thread/82/fund-categories


Addendum, 5/30/22. For the 3 funds in the M* example, FKIQX (nominal equity 38.59%, new M* MPRS 68.81%, Effective Equity 63.67%), RBBAX (20.44%, 44.21%, 44.75%), ACEIX (63.47%, 88.26%, 82.42%), both M* MPRS and Effective Equity systems lead to 1-notch bump ups in their respective categories. For OAKBX (61.20%, 92.97%, 85.96%), both systems would indicate 2-notch bump ups, but M* did only 1-notch bump up in its category. For FAIRX (88.47%, 110.27%, 132.21%), M* old and new categories don't make sense. It seems that regardless of the new M* MPRS data, M* has done just 1-notch bump ups and that may have been a business decision. In these evaluations, all data used are to 4/30/22 (M*, PV).

In an earlier example in this thread, DODBX (formerly among the most aggressive allocation/balanced funds) was used as an example. But this fund has recently changed its objectives/strategies to include short positions, rather unusual for an allocation/balanced fund. That has caused it to perform quite differently from its peers in 2022. So, the success or failure of its new strategy would have to be reviewed in future.

Addendum2, 6/5/22. Found M* MPRS - M* Portfolio Risk Scoring Methodology and related Empirical Analysis (with several examples) documents from October 2021! (M* keeps going back-and-forth on web-links and download-only-links for its methodology documents)

M* Link (download)  

M* Link2 (download)

Edit/Add, 4/8/24. In the final implementation of MPRS, M* is using its own opaque risk models and other factors (returns, volatilities) to determine portfolio risk scores with multiple methodologies. Those scores are normalized with the value 100 assigned for the upper limit of Very Aggressive portfolios on an absolute scale. A mapping table is then developed. The specific MPRS numbers for funds are displayed in the M* Risk tab, but  those numbers don't have good intuitive meaning by themselves.

Conservative          0-24
Moderate               24-48
Aggressive             48-79
Very Aggressive     79-100
Extreme Risk         100-200

As an example, 60-40 VBINX has a risk score of 43 and it doesn't change whether 3, 5, or 10 years are clicked.
www.morningstar.com/funds/xnas/vbinx/risk

So, this system is no longer like the YBB Relative SD (or, Effective Equity), or the original MPRS notion of Relative Beta, that rely on benchmarks and tend to be more stable because the market conditions affect both the funds and the benchmark.

MPRS, 03/2023 (download)
MPRS, 03/2024 (download)
PDF Host - MPRS, 03/2024
pdfhost.io/v/fTm~1TZwhz_MStar_MPRS_032024

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Multi-Assets Funds - Performance, Beta, Standard Deviation

M* article on multi-asset funds analyzes their behavior in the downdrafts of 2020 and 2022 by looking at their performance, beta (used by M* for recent revisions in their categories - see MPRS) and standard deviation (used for Effective Equity). M* conclusion is that multi-asset funds did worse then expected in 2020 and better than expected in 2022.

M* also notes that now such funds are found in several M* categories - allocation/balanced, global/world-allocation, tactical-allocation, multisector bond funds. While M* doesn't have a separate category for multi-asset funds, it does have a Multi-Asset Income (MAI) - Institutional category with several dozen funds that also are in several M* categories.

Unfortunately, some of the issues that M* pointed out may be related to monthly data used by M* and PV for calculating MPT statistics and the situation may improve if weekly data were used for MPT statistics.

www.morningstar.com/articles/1097243/multi-asset-income-funds-is-the-extra-income-worth-the-extra-risk


EDIT/ADD: Twitter LINK

"YBB Personal Finance
@ybb_Finance
3m
Replying to
@ybb_Finance

#MPT stats based on monthly data used by #MorningstarInc & #PortfolioVisualizer, etc have limitations. To improve sensitivity, weekly (if not daily) data should be used."

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Twitter LINK

YBB Personal Finance
@ybb_Finance
6m   (7/7/22)

#RiskControl is the key for sound #PortfolioAllocation /management. While many debate endlessly what #risk is, any decent risk/#volatility measure will do. My favorite is #RelativeSD. #MorningstarInc recently introduced #MPRS that is primarily based on #RelativeBeta.

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Modified Strategy

I am making some changes in strategy because of changed availability of data.

BACKGROUND. Use of Effective-equity involved maintaining M* Portfolio and using allocation % in PV. When portfolio wasn't maintained at M* Portfolio, allocation % were obtained directly from brokerage/fund websites. Status of M* Portfolio is in limbo. Although its discontinuation date seems to have been delayed, it is unclear what portfolio capabilities the new M* Investor will eventually have.

So, I have recently switched over to Stock Rover (SR) Premium. It provides data for beta and standard deviation based on daily returns (vs monthly returns used by M* and PV) but the information provided by SR is less than ideal. There are 2 issues: i) SR beta and SR SD are weighted-averages of component values, but that overestimates their values as cross-correlations among components are not accounted for, and ii) inconsistent use of weighted-averages - SR allocation % uses all components, but SR beta ignores money-market funds, and SR SD ignores both money-market funds and cash (a puzzling SR software inconsistency).

Bottomline is that SR beta may be more accurate than SR SD although both are imperfect. Of course, both can be adjusted (by different factors). If a portfolio doesn't have any money-market funds and/or cash, then adjustments to SR beta and SD won't be needed. 

I have also commented on new M* MPRS that are based on Relative-beta (not Relative-SD). The results are generally similar. 

NEW STRATEGY. For accurate assessment of Effective-equity, use PV with allocation % from SR or brokerage/fund data. This can be done quarterly, or after major portfolio changes.

But for interim portfolio monitoring, use imperfect SR SD and SR beta to determine Relative-SD (Effective-equity) and Relative-beta. If portfolio has high % of money-market funds and/or cash, then make appropriate adjustments for those. Keep in mind that these interim relative values will be higher than actual relative values, but this interim monitoring can be done anytime without much effort.

Edit/Add: The SR was contacted about these issues (with the m-mkt funds and cash in weighted-averages) and after some back-and-forth correspondence, they were fixed on 10/17/22.

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Relative SD, Relative Beta & Adjusted Relative SD

Relative SD, SD/SDb = beta/r

Portfolio SD calculation is difficult, e.g. from direct SD calculation of the portfolio performance, or from direct regression analysis of the portfolio and benchmark performances. Many sites such as Stock Rover (SR) use just the weighted-average of component SDs, but that overestimates the SD (by ignoring cross-correlations). Unfortunately, SR does the same with beta, i.e. it calculates portfolio beta from the weighted-average of component beta.

M* recently proposed Relative Beta as the MPRS – M* Portfolio Risk Score

Also note that , SR (SD/SDb) >= SR beta

So, a consistent but variable downward adjustment to SR (SD/SDb) may be by averaging the SR (SS/SDb) and the SR beta.

Average = 0.5 (SD/SDb + beta) = 0.5 (beta/r + beta) = 0.5*(1+r)*beta/r = 0.5*(1+r)*SD/SDb

So, Adjusted (SD/SDb) = 0.5*(1+r)*SD/SDb

Note that for r = 1, the Adjusted (SD/SDb) and Relative SD, SD/SDb, are the same. But their difference rises as r << 1.

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Mean, SD & Normalization

There is an interesting exchange at PB-Big Bang about mean & SD (@chang & @yogibearbull),
big-bang-investors.proboards.com/thread/3086/volatility-standard-deviation-risk

As SD is around a mean, why not use them as pair vs using only SD?

First, if one wanted to do that, then SD as % of mean is the inverse Sharpe Ratio.

Second, consider normalization of the data series.

Add an arbitrary constant C to a data series Xi with mean Xbar and SD. The new mean is Xbar + C, but SD is unchanged.

So long as C is arbitrary, why not set it to produce a mean of 0? Some may call it normalization.

Or, why not consider a data series of (X - Xbar) ? Then, the mean is 0, and SD is unchanged.

I think that is why the business & finance started looking into SD in isolation.

This may be arcane, but I use Relative SD, or SD/SDbenchmark, as a critical criterion, and have named it Effective-Equity, so I had to resolve this question.

Edit/Add, More.
big-bang-investors.proboards.com/post/48070/thread

(yogibearbull, 3/8/24)

M* SD is not on prices, but on % monthly returns. This is a common practice in finance & MPT. So, the data series is that of monthly total returns, and the SD is also that of monthly returns around the mean monthly return. Then, the SD is annualized by multiplying by sqrt(12) to get the annualized SD. So, the units of SD naturally are % whether indicated or not. Stock Rover (SR) provides SD as 0.XX which is SD/100; it initially confused me because the SR numbers weren't in the ball park with those at M* or PV. Then I found that SR used daily returns, not monthly returns, and that is why SR SD values are generally higher than those at M*, PV, etc.

Sharpe Ratio is Excess Mean/SD, but close enough would be Mean/SD. Excess Mean is Mean minus safe yield (typically, 3-mo T-Bills)

What @chang , is saying/wants, then, is the inverse Sharpe Ratio, or SD/Mean. If one plays around with it a bit, one will find that it isn't of much practical use.

All about M* MPT can be found in this document,
pdfhost.io/v/IADc7lkOZ_MStar_MPT_1209644_030824

BTW, Bollinger Bands are calculated with prices and are +/- 2*SD bands around prices; the timeframe is also short, only 20 trading days, but the parameters can be adjusted in StockCharts. I often look at Bollinger Band Width (BBW) that is basically 4*SD on prices (see Bottom panel).
stockcharts.com/h-sc/ui?s=%24SPX&p=D&yr=3&mn=0&dy=0&id=p05518374476