EigenScore
EigenScore
You are given the daily returns of n assets over T days as a T x n matrix R, where R[t][i] is the return of asset i on day t.
A weight vector w with w_1^2 + ... + w_n^2 = 1 defines the portfolio return series p_t = R[t][1] w_1 + ... + R[t][n] w_n. Find the w for which the sample variance of p_1, ..., p_T is smallest.
To fix the sign, output the w whose component of largest absolute value is positive.
The first line contains T and n. Each of the next T lines contains n real numbers, the returns of that day, each with at most 6 digits after the decimal point.
n real numbers w_1, ..., w_n, each with absolute or relative error at most 1e-9.
2 <= n <= 20
n + 1 <= T <= 400
It is guaranteed that the minimizing direction is unique.
This is a standard problem: a submission scores full points if it produces the correct output for every test case, and zero otherwise.
Numeric answers are accepted if they are within an absolute tolerance of 1e-09 or a relative tolerance of 1e-09 of the expected value.
6 2 -0.011124 0.000445 0.018100 -0.010024 -0.023667 -0.001467 0.031836 -0.002040 -0.046964 -0.012130 -0.014521 -0.012268
-0.06141763299817512 0.9981121551994552
30 4 0.017833 -0.006588 -0.020016 0.018444 -0.003903 0.014853 0.034964 0.013398 0.021261 -0.001811 0.004596 -0.008254 -0.001396 -0.003081 0.005057 -0.011317 0.022948 -0.023261 0.005904 -0.005468 0.005359 0.028984 -0.000215 -0.002594 0.036346 0.019880 -0.032758 0.000278 -0.028406 -0.015031 0.026713 -0.009070 0.014319 -0.030345 0.007413 0.020697 0.001872 0.003964 -0.016865 -0.003254 -0.023080 0.030619 0.001388 0.007729 0.010194 0.015921 -0.002412 -0.009755 0.006679 -0.009638 0.023173 -0.009211 -0.000398 -0.003802 0.015664 0.015092 0.028165 0.027106 0.009716 -0.005942 -0.014228 0.033975 -0.009043 -0.003681 -0.013508 -0.033361 -0.014826 0.017948 0.004739 -0.038965 -0.044204 0.000487 -0.012034 0.035392 -0.004542 0.020504 0.043090 -0.002481 0.022983 0.001128 -0.019112 -0.015831 0.013556 0.019389 -0.006429 -0.003918 -0.009243 -0.004996 0.010174 -0.017671 0.009504 0.010397 -0.013375 -0.020296 0.009360 0.002876 -0.018550 -0.026943 -0.063568 -0.018978 -0.012189 -0.004616 0.008808 0.013261 0.001670 -0.042639 -0.008760 0.013746 -0.003211 -0.000477 -0.008774 0.015583 0.014868 0.005865 0.051483 0.007773 -0.017663 -0.016382 -0.009257 -0.002155
0.09942063951195336 0.09232502966663914 -0.15930603028539678 0.9778615515760893