Research interview statistics round.
The third correlation
The question
A and B are 0.9 correlated, B and C are 0.9 correlated. What range is possible for the correlation of A and C?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
From 0.62 to 1.
Correlations are constrained because the correlation matrix must be positive semi-definite.
For three variables the bound is rho_AC between rho_AB times rho_BC minus sqrt((1 - rho_AB^2)(1 - rho_BC^2)) and the same product plus that root.
With both at 0.9 the product is 0.81 and the root term is 0.19, giving the interval 0.62 to 1.
The intuitive reading is that correlation is close to an angle between vectors: two vectors each close to B cannot be far from each other.
What it is testing
Whether you know correlation matrices carry geometric constraints.
Try these next
Why the top performers disappoint
Warm-upA fund's best traders this year are usually worse next year. Does that mean the firm is failing to develop them?
How long to trust a Sharpe ratio
HardA strategy shows a Sharpe of 2 over six months. How much should that convince you?
The backtest that will not survive
StandardYou tried two hundred signal variants and kept the best. Its backtest Sharpe is 2.5. What do you actually believe?
Is this series stationary?
StandardWhy does stationarity matter before you model a price series, and what do you do about it?
Preparing properly
Live opportunities
Interviewing soon? See who is hiring
Open vacancies we track at quant firms, grouped by role and city. Adverts are anonymised.
Hiring for these roles? Brief the desk on a hire or check your fit for a role.
Research desk
Speak to a quant market specialist
Ask what a firm really pays, how a desk hires, or where your profile sits. One reply from the research desk, in confidence, no obligation.