Factors are underlying sources of systematic risk that help explain the returns of assets. In finance, a factor represents a measurable characteristic, such as market risk, size, value, or momentum that influences asset returns.
Factor regressions are used to model how much of an asset’s return can be explained by exposure to these factors. For example, two different stocks may move together not because they are directly related, but because they are both exposed to the same underlying factor, such as overall market movements or economic conditions, see this for more info
Extending the Capital Asset Pricing Model(CAPM) formula from Market Efficiency
here \alpha is manager over/under performance
Cap Weighted Index Fund vs Equal-Weighted Index Fund:
- A cap-weighted index fund allocates more weight to companies with higher market capitalization. This means large companies have a bigger influence on the index’s performance. It reflects the market’s consensus value and requires minimal rebalancing, making it cost-efficient. However, it can become concentrated in a few large stocks and may overexpose investors to overvalued companies
- An equal-weighted index fund gives the same weight to all companies, regardless of their size. Each stock contributes equally to the overall performance. This approach provides better diversification and higher exposure to smaller companies. However, it requires frequent rebalancing, leading to higher costs and turnover
Skewness:
- Skewness measures the asymmetry of a distribution of returns around its mean. It tells us whether extreme outcomes are more likely on one side of the distribution
- Positive skewness means the distribution has a longer right tail, indicating a higher chance of large positive returns. Negative skewness means a longer left tail, indicating a higher risk of large losses
- Simply, this means returns are not evenly distributed, a few extreme outcomes (big wins or big losses) can dominate overall performance, this goes with the famous index fund quote “don’t search needle in a haystack, buy the haystack”