MPT - Modern Portfolio Theory

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The MPT statistics are simply the linear regression statistics that were applied to portfolio analysis in 1950s. The statistical concepts are quite old. For example, the term standard deviation (SD) goes back to 1893 and the notion of root-mean-square-error/deviation (RMSE/RMSD) is even older; similar for correlation r.

Among the MPT statistics, Alpha is very unstable. It is highly affected by time periods, portfolio mix, and benchmark used. On the other hand, SD and correlation (r) are quite stable. As mentioned elsewhere, beta, r and SD are related as,

SD/SD_benchmark = beta/r

These linear regression based MPT statistics are meaningful only when correlation r is high.

Edit/Add, 3/8/24. M* MPT document has definitions and explanations of MPT terms.
PDF Host Link  pdfhost.io/v/IADc7lkOZ_MStar_MPT_1209644_030824
PB Attachment
MStar_MPT_1209644_030824.pdf (270.07 KB)

www.edge.org/response-detail/25401#:~:text=It%20is%20all%20due%20to,thought%20it%20meant%20mean%20deviation.
en.wikipedia.org/wiki/Standard_deviation
en.wikipedia.org/wiki/Root_mean_square
en.wikipedia.org/wiki/Root-mean-square_deviation
en.wikipedia.org/wiki/Modern_portfolio_theory
www.investopedia.com/articles/07/portfolio-history.asp

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Fund Alpha is Overrated – M* JR
www.morningstar.com/articles/963345/whats-alpha

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M* JR: Beta is Back / Beta Isn't Dead
www.morningstar.com/stocks/beta-isnt-dead

Twitter LINK
YBB Personal Finance
@ybb_Finance
(1/30/24)

1/2 Interesting take on #Beta.
Significance of early work on #MPT was its application of #Statistics to investments. Slope ("beta") & intercept ("alpha) of #LinearRegression were already ancient concepts then.

YBB Personal Finance
@ybb_Finance
(1/30/24)

2/2 Now they are commonly available tools. #Morningstar won't exist without such tools.
Sharpe's claim to fame is the #SharpeRatio that interestingly doesn't depend on MPT - #StandardDeviation can be found directly (& is more stable than beta).

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Alpha, Beta, Sharpe Ratio
www.mutualfundobserver.com/discuss/discussion/comment/174391/#Comment_174391

yogibearbull  (4/3/24)

MPT stats Alpha and Sharpe Ratio (in the PV runs, Metrics tab) also capture the essence of the comparative evaluation of funds with their beta-bogeys (beta% in appropriate benchmark).

Alpha > 0 means that fund outperforms its beta-bogey, alpha = 0 means that fund just keeps up with the beta-bogy, and alpha < 0 means that fund underperforms the beta-bogey.

Indirectly, these will also have, correspondingly, Sharpe Ratios of high, OK, low.

Beta-bogeys would be different for US stocks (SPY), US bonds (AGG?) and foreign stocks (VXUS?).

Unfortunately, PV doesn't provide options for bogeys. Its default bogey is SP500/SPY.
Correction. ybbpersonalfinance.proboards.com/post/1423/thread

Morningstar has a few built-in bogeys, but those aren't selectable by users. Check M* Risk tab.

Edit/Add. MFO Premium Watchlist (extended results) show fund beta with respect to SP500 AND Best-Fit-Benchmark (BF-BM), but BF-BM are NOT identified. MFO Premium doesn't provide this info for funds or portfolio.

So, some limitations aren't conceptual, but those of the analytics software used.