# Investment EMH

## The Stock Market is Efficient

- Only a minority of actively managed mutual funds beat the S&P index Active management Liu.
- Roughly half of "mutual funds" are actually "closet indexers" - essentially index funds that are technically "actively managed" to justify higher fees Active management.

## International Financial Markets are Not Efficient

**Equity home bias puzzle**- Most investors hold small amounts of foreign equity despite having a comparative advantage doing so. That being said, this irrational bias has shrunk over time. Equity home bias puzzle**Feldstein–Horioka puzzle**- assuming perfect capital mobility, there should be minimal correlation between the amount of savings by a country and the amount of investment in that country. In reality, however, there is significant correlation Feldstein–Horioka puzzle.

## My Analysis

I looked at 100 stock's daily returns from 1984 to 2017 Marjanovic and modeled each daily price move as

```
Y_it = B_0 + B_i1 + B_i2 * X_t + B_i3 * Norm()
```

where `Y_t`

is stock `i`

's daily return, `X_t`

is the normalized change in the overall stock index, `B_0`

is the average index return, and the three `B_i`

parameters represent alpha, beta, and idiosyncratic risk, respectively.

Of the 100 stocks, 4 rejected the null-hypothesis that `B_i1=0`

. I'd expect 5 to reject the null-hypothesis by chance alone, so this is to say that I found no statistical evidence that any stock reliably beats the market.

This is actually puzzling because 89 of the stocks rejected the null-hypothesis that `B_i2=1`

, which means that many of these stocks did have different levels of risk. Moreover, `B_i3`

didn't correlate with `B_i2`

, which means stocks with high systematic risk (beta) also tended to have high idiosyncratic risk.

This raises the question: why does anyone invest in high-beta stocks if there's no evidence they compensate their owners with higher returns or even lower idiosyncratic risk?