I don’t have a good intuition about how costly this actually is in practice, if you only play with 10% of your portfolio.
tl;dr extremely little.
Here’s some numbers I made up:
Let the market’s single common factor explain 90% of the variance of each stock.
Let the remaining 10%s be idiosyncratic and independent.
Let stocks have equal volatility (and let all risk be described by volatility).
Now compare a portfolio that’s $100 of each of a hundred stocks with one that’s $90 of each of a hundred plus $1k of another stock. (I’ll model each stock as 0.75 times the market factor plus 0.25 a same-variance idiosyncratic factor.) Compared to a $10k single-stock portfolio...
the equal-weighted portfolio has σ like √(75∗100)2+252∗100√75002+25002≈0.9492
the shot-caller’s portfolio has σ like √(81∗100+900)2+22.52∗100+2502√75002+25002=0.9496
...for an increase in σ of 4.5 basis points. So, pretty negligible.
Even if the market’s single factor explains only half of the variance of each stock, the increased risk of the shot-caller’s portfolio is just 40 basis points (0.7135 vs 0.7106). In the extreme case where stocks are uncorrelated, the increased risk is +34.5%, though I think that that’s unrealistically generous to the diversification strategy.
Since an increase in volatility-per-dollar of x basis points means that you give up x basis points of your expected returns, I’m going to say that this effect is negligible in the “10% of portfolio” setting.
tl;dr extremely little.
Here’s some numbers I made up:
Let the market’s single common factor explain 90% of the variance of each stock.
Let the remaining 10%s be idiosyncratic and independent.
Let stocks have equal volatility (and let all risk be described by volatility).
Now compare a portfolio that’s $100 of each of a hundred stocks with one that’s $90 of each of a hundred plus $1k of another stock. (I’ll model each stock as 0.75 times the market factor plus 0.25 a same-variance idiosyncratic factor.) Compared to a $10k single-stock portfolio...
the equal-weighted portfolio has σ like √(75∗100)2+252∗100√75002+25002≈0.9492
the shot-caller’s portfolio has σ like √(81∗100+900)2+22.52∗100+2502√75002+25002=0.9496
...for an increase in σ of 4.5 basis points. So, pretty negligible.
Even if the market’s single factor explains only half of the variance of each stock, the increased risk of the shot-caller’s portfolio is just 40 basis points (0.7135 vs 0.7106). In the extreme case where stocks are uncorrelated, the increased risk is +34.5%, though I think that that’s unrealistically generous to the diversification strategy.
Since an increase in volatility-per-dollar of x basis points means that you give up x basis points of your expected returns, I’m going to say that this effect is negligible in the “10% of portfolio” setting.