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

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