# How to get twice the expected return of S&P 500

If I create a diversified portfolio of 2*beta stocks, can I expect to get twice the return of S&P 500.

Example: Out of the universe of stocks available to me I randomly choose 10 stocks whose betas are 2. For a year if S&P 500 got 10 %, does that mean I will make 20 % in my portfolio. Reverse is true as well, if S&P made -10 %, I will make -20%.

Do these statements make sense ?

Thanks. Coder

If you want to obtain 2 times the S&P 500 return, it's safer just buying a leveraged etf tracking the index. Randomly chosing 10 stocks obtaining a 2 beta position can lead to different results. You will have a tracking error due to the leftover idiosyncratic risk

In theory, if you create a fully diversified portfolio with $\beta=2$ you should get 2 times the risk premium on the market. In practice the SML of the CAPM is too flat, meaning that you would be better off buying low beta stocks and shorting high beta stocks. If you don’t trust me read Betting Against Beta by Andrea Frazzini and Lasse Haje Pedersen.They say in the abstract:

We present a model with leverage and margin constraints that vary across investors and time. We find evidence consistent with each of the model's five central predictions: (1) Because constrained investors bid up high-beta assets, high beta is associated with low alpha, as we find empirically for US equities, 20 international equity markets, Treasury bonds, corporate bonds, and futures. (2) A betting against beta (BAB) factor, which is long leveraged low-beta assets and short high-beta assets, produces significant positive risk- adjusted returns. (3) When funding constraints tighten, the return of the BAB factor is low. (4) Increased funding liquidity risk compresses betas toward one. (5) More constrained investors hold riskier assets.