Final answer:
The portfolio consisting entirely of bonds (weightS&P = 0%, weightBond = 100%) has the lowest risk due to bonds having lower volatility compared to stocks. However, this portfolio also has lower expected returns, highlighting the risk-return tradeoff inherent in investment choices.
Step-by-step explanation:
When creating different investment portfolios with varying weights on the S&P 500 index and bonds, we recognize that as the weight in stocks (weightS&P) increases, the potential for higher returns also increases, but so does the risk. Conversely, a higher weight in bonds (weightBond) implies lower risk but also lower returns. To determine the portfolio with the lowest risk, we calculate the standard deviation for each, with weightBond being 1 minus weightS&P for weights ranging from 0% to 100% in increments of 10%.
The portfolio with 100% in bonds (weightS&P = 0%, weightBond = 100%) will typically have the lowest risk, given that bonds fluctuate less in value compared to stocks and generally provide more stable returns. However, the tradeoff is that this portfolio also usually offers lower expected returns compared to a portfolio with a higher allocation to stocks.
This is in line with the general investment principle that there is a tradeoff between risk and return; assets with higher potential returns, like stocks, also come with higher risk. The converse is also true; investments with lower risk, like bonds, typically offer lower returns. This risk-return tradeoff is fundamental to the investment decisions that individuals and households make.