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Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i.e., the risk). [1] The efficient frontier was first formulated by Harry Markowitz in 1952; [2] see Markowitz model.
The return - standard deviation space is sometimes called the space of 'expected return vs risk'. Every possible combination of risky assets, can be plotted in this risk-expected return space, and the collection of all such possible portfolios defines a region in this space.
In other words, investors should expect a higher return on an investment when that investment carries a higher level of risk or uncertainty. When evaluating investments, investors should estimate both the expected return and the uncertainty of future returns. Standard deviation provides a quantified estimate of the uncertainty of future returns.
An investment’s “expected return” is a critical number, but in theory it is fairly simple: It is the total amount of money you can expect to gain or lose on an investment with a predictable ...
All this can be visualised by plotting expected return on the vertical axis against risk (represented by standard deviation upon that expected return) on the horizontal axis. This line starts at the risk-free rate and rises as risk rises. The line will tend to be straight, and will be straight at equilibrium (see discussion below on domination).
The slope of the capital allocation line is equal to the incremental return of the portfolio to the incremental increase of risk. Hence, the slope of the capital allocation line is called the reward-to-variability ratio because the expected return increases continually with the increase of risk as measured by the standard deviation.
The average magnitude of the observations is merely an approximation of the standard deviation of the market index. Assuming that the market index daily changes are normally distributed with mean zero and standard deviation σ, the expected value of the magnitude of the observations is √(2/ π)σ = 0.798σ. The net effect is that this crude ...
And a chart in Goldman Sachs' 2024 US Equity Outlook shows that's the largest portion of S&P 500 market cap ever dominated by just seven ... "The 7 stocks have faster expected sales growth, higher ...