Perfect Negative Correlation - How Does this Make Money?

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swaggerer

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In the Portfolio Management readings, it is said that perfect negative correlation is a sort of ideal scenario, because it reduces the risk (standard deviation) of the portfolio to zero. For example, in a two stock portfolio, when one stock moves up, the other moves down by the same amount, and vice versa. But I’m confused - how does this actually make money? Wouldn’t the two stocks cancel each other out (e.g., one goes up $10 and the other goes down $10), leaving you with a return of zero?
 
Consider that each stock in portfolio can have perfect negative correlation with another but each stock has different standard deviation as a measure of its own risk. Also consider long term portfolio and various Economic outlook (recessions, expansions, stable outlook) what means that in one period one stock can be portfolio return driver and in another period (ex. recession) another stock (or bond) takes the role of portfolio anchor reducing losses.
 
You’re a victim of the sloppy language of people in finance.
First, when you talk about correlation, you need to be specific about what characteristics are correlated. Do not ever – ever! – say, “the correlation of two stocks.” Ever!
If you mean the correlation of the stocks’ prices, then say the correlation of stocks’ prices. If you mean the correlation of the stocks’ returns, then say the correlation of the stocks’ returns.
(Similarly, do not say “the standard deviation of the portfolio.” If you mean the standard deviation of the portfolio’s prices, then say the standard deviation of the portfolio’s prices. If you mean the standard deviation of the portfolio’s returns, then say the standard deviation of the portfolio’s returns.)
Second, remember that correlation measures how two quantities move about their respective means, not about zero. If you have perfect, positive correlation, the quantities are above their respective means together, and below their respective means together. If you have perfect, negative correlation, one quantity is above its mean when the other is below its mean, and vice-versa.
Third, remember that in portfolio management, we’re talking about the correlation of returns, and the standard deviation of returns, not the correlation and standard deviation of prices. These are very, very different ideas. Two stocks can have perfect, positive correlation of returns and:
  • Perfect, positive correlation of prices,
  • Zero correlation of prices, or
  • Nearly perfect, negative correlation of prices
It all depends on what the respective mean returns are.
Try an experiment in Excel. Start with two stocks – A and B – priced at $100/share. For 20 periods, let the periodic returns be:
  • A: +2%, 0%, +2%, 0%, … ; B: +2%, 0%, +2%, −0%, …
  • A: +2%, 0%, +2%, 0%, … ; B: +1%, −1%, +1%, −1%, …
  • A: +2%, 0%, +2%, 0%, … ; B: 0%, −2%, 0%, −2%, …
In all three cases, the correlation of returns is +1.0. Take a look at the prices.
 
Flashback wrote:Consider that each stock in portfolio can have perfect negative correlation with another but each stock has different standard deviation as a measure of its own risk. Also consider long term portfolio and various Economic outlook (recessions, expansions, stable outlook) what means that in one period one stock can be portfolio return driver and in another period (ex. recession) another stock (or bond) takes the role of portfolio anchor reducing losses.
Click to expand...
You’re missing the most important point: that correlation of returns and correlation of prices are two completely different ideas.
 
S2000magician wrote:
Flashback wrote:Consider that each stock in portfolio can have perfect negative correlation with another but each stock has different standard deviation as a measure of its own risk. Also consider long term portfolio and various Economic outlook (recessions, expansions, stable outlook) what means that in one period one stock can be portfolio return driver and in another period (ex. recession) another stock (or bond) takes the role of portfolio anchor reducing losses.
Click to expand...
You’re missing the most important point: that correlation of returns and correlation of prices are two completely different ideas.
Click to expand...
OK, thanks for letting me reminded. I am not a mathematician so unfortunately I am not able to explain it in understable and plain language.:)
 
Flashback wrote:
S2000magician wrote:
Flashback wrote:Consider that each stock in portfolio can have perfect negative correlation with another but each stock has different standard deviation as a measure of its own risk. Also consider long term portfolio and various Economic outlook (recessions, expansions, stable outlook) what means that in one period one stock can be portfolio return driver and in another period (ex. recession) another stock (or bond) takes the role of portfolio anchor reducing losses.
Click to expand...
You’re missing the most important point: that correlation of returns and correlation of prices are two completely different ideas.
Click to expand...
OK, thanks for letting me reminded. I am not a mathematician so unfortunately I am not able to explain it in understable and plain language.:)
Click to expand...
It’s not your fault: finance people are incredibly sloppy. They confuse correlation of returns and correlation of prices all the time.
 
I like your lessons but sometimes I need my maths and econometric
textbooks to follow and understand your answers.
 
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