# The milestone of finance: risk-return trade-off

## The Basic Trade-Off

Unfortunately, it is not possible to achieve both targets

- Pretty always, higher return corresponds to higher risk
- Very safe investments give lower return

Derivative instruments (options,futures,CDS), sovereign bonds of distress country, stock of

new company

German Bund, US Treasury Bonds, stock of mature company (e.g., Enel, Eni), bank deposit

It is called the Trade-Off between Risk and Return - It may be considered as the Basic Stone of Finance

In practice, what we can do, is - Maximize the Expected Return, given a certain Risk
- Minimize the Expected Risk, given a certain Return

## From Efficient Frontier to CAL

We can define a risk-free asset as follows

It has zero-variance in returns

It is uncorrelated with any other asset (as zero-variance)

- It pays a risk-free rate of return

Safe Gov. Bonds are used as risk-free assets (Treasury Bills, German Bunds, Bank Deposit)

The introduction of the risk-free asset makes wider our investment opportunities

1 We can invest in the risk-free asset (buying government bonds, leaving money in the bank)

2 We can borrow at the risk-free rate of return (shorting gov. bonds, borrowing money from

bank) - Then, we can combine risky strategies (optimal portfolios) with risk-free investment
- We derive a New Efficient Frontier

Raffaele