MPT assumptions:
1.) risk it synonymous with volatility; that they are the same thing and volatility can be substituted for risk in MPT's calculations
2.) The markets are always efficient and immediately incorporate into the market price all known information either in the strong (perfect) or weak (essentially) sense, causing a financial asset to have one true value at any point in time which is it's market price.
3.) that the future volatility for an asset will be essentially the same as past volatility for that asset
4.) that past returns of an asset class are a reasonable predictor of the future returns +/- the volatility inherent in an asset
5.) that the future level of correlation between two assets will be the same as past correlation between those two assets
6.) That the ideal portfolio is one which attempts the highest risk-adjusted (i.e. volatility adjusted) returns for an investor's desired risk-tolerance (i.e. volatility-tolerance). An investor does this looking to past data, e.g. by taking into account past returns, past volatility, and past correlation between assets.
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LAS, I think you see it as MPT VS value investing. They aren't mutually exclusive, and they don't contradict each other. MPT is a tool, not a religion. MPT is a tool to compare investments, asset classes, and portfolios based on their risk VS return trade off. It's just trying to create a measuring stick where there wasn't one. I also think you might be confusing Efficient market hypothesis with MPT. They are different things.
1) Risk according to MPT is the risk that you get returns different from what you expect. You expected 10%, and got 8%, that is a risk of lower than expected returns. Volatility is one way to measure how likely your returns will be different. Volatility tends to go both ways, up and down. If you're worried about getting returns less than what you expected, volatility isn't a bad thing to look at. Most formulas in MPT are comparing an investment, asset class, or an entire portfolio to a hypothetical risk free option. Is the extra return over the risk free rate worth the extra volatility that was added? Markowitz theorized that was a good way of taking something incredibly complicated(at the time) and converting it into a useful measuring stick.
2) You are talking about Efficient Market Theory here, not MPT. None of this applies to MPT.
3) It's a tool, not a religion. The person doing the calculation can substitute a different number. In most cases all you will have is past data, so yes, that does get used a lot.
4) Again, it's a tool, not a religion. The person doing the calculation can substitute a different number.
5) It's a tool. You can apply common sense. Example: US Stocks and US treasuries tend to move in different directions during crisis events thanks to flight to quality. If that was called into question you could use a different number.
6) Most investors don't like to see their portfolio drop 50%. Many investors would panic in that event and make impulsive(stupid) decisions. If a more moderate portfolio can achieve similar returns with substantially less downside then those investors will likely be better off with the moderate portfolio. Depending on when you need the money you might want to avoid big drops for logical reasons as well.
Value
1) You need to stay above inflation? MPT wants you to stay above the risk free rate. Just plug inflation in as your risk free rate, which many investors do, and you are describing the same thing.
2) Okay. None of this conflicts with MPT.
3) Okay. I agree with everything you said. I like value investing and I like MPT as a tool. None of this conflicts with MPT. Again, I think your complaint is with EMH, not MPT.
4) Okay. Buy things that are likely to give you higher returns without taking on substantial risk. How does this conflict with MPT? MPT actually has calculations that help you measure how well you are doing this VS a benchmark of your choosing.
5) It's not a religion. Use common sense and readily available data. If facebook and Telsa both go down on the same day, it's likely chance or they are both moving with the overall market. If VOO and SPY both move in the same direction 100% of the time... it might be because they are tracking the same index. Is there a cause and effect relationship? No, then it's chance. Yes, how strong is that relationship and will it continue? Again, MPT is a tool to be used. It's not a religion. If there is a cause and effect relationship, use it as long as it makes sense.
6) To summarize what you said: an investor builds a portfolio based on their income needs while limiting the amount of risk they are taking. You are constructing a portfolio with the understanding that you want to earn money but you don't want to take on excessive risk. That's the basis of MPT...