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Quantitative Research Interview Questions
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Given the daily return for past year(approximately 250 trading days) of the 500 componential stocks from S&P 500, we have 500*499/2 = 124750 correlation coefficients, What is the distribution of these coefficients? 1. Is it symmetric? 2. Is it shifting to the right or changing its shape? 3. Does it have a fatter tail than Gaussian? Why? 4. How to estimate the correlations? 5. Give me an estimate of the expectation of the correlations.
Suppose we have a polynomial f(x) with real coefficients {a0,a1,...,an}of degree n unknown, we could input x and get the output f(x). 1. What is the minimum trials of input to get all coefficients? 2. What if all coefficients are integers? 3. What is all coefficients are positive integers?
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