# 8-1 Portfolio Theory and CAPM â€‹

## Portfolio Theory â€‹

- reduce the
*standard deviation*of a portfolio by choosing stocks that do not move together.

when measured over a short interval, the past rates of return on any stock conform closely to a normal distribution.

normal distributions can be completely defined by two numbers:

- the mean or expected value.
- the variance or standard deviation.

In this chart:

- A and B
- have the same
*expected*return of`10%`

- A has the greater spread of possible returns ergo it's more risky than B.
- the spread can be measured by the standard deviation
`std(A) = 15%`

`std(B) = 7.5%`

- most investors would prefer B to A.

- have the same
- B and C
- have the same
*standard deviation* - C offers a higher expected return.
- most investors would prefer C to B.

- have the same

### Efficient Portfolios â€‹

Efficient Portfolios

Efficient portfolios are combinations of investments that maximize their overall returns within an acceptable level of risk.

Finding the best efficient portfolio

With a graph of the efficient portfolios, draw a line starting at the risk free return *ratio* of risk premium to standard deviation.

#### Borrowing and Lending â€‹

If investors have access to borrowing and lending at the risk-free rate, then the investor can obtain any combination of risk and return **along the tangent line** by either borrowing money which is then invested in the best efficient portfolio(=more risk) or lending money (=less risk).

example

The best efficient portfolio S has `std=16%`

, `r=15%`

.

- Less risk less return strategy:
- invest half in S
- lend the rest at the risk-free rate.

- More risk more return strategy:
- borrow initial amount.
- invest all in S

Sharpe Ratio

The ratio of the risk premium to standard deviation. the best efficient portfolio has the highest sharpe ratio.