Sharpe Ratio and related calculations.

sharperatio.lisp

(defun mean (sequence)
  (/ (reduce #'+ sequence) (length sequence)))

(defun variance (sequence)
  (let ((m (mean sequence))
        (n (length sequence)))
    (/ (reduce #'+ (map 'vector (lambda (x) (expt (- x m) 2)) sequence))
       (length sequence))))

(defun std-dev (sequence)
  (sqrt (variance sequence)))

;; in which we assume RETURNS is a vector of double floats
(defun sharpe-ratio (returns &optional (rfree 0.02))
  (when (zerop (length returns))
    (return-from sharpe-ratio 0))
  (let ((mean-return (mean returns))
        (sd (std-dev returns)))
    (when (zerop sd)
      (return-from sharpe-ratio 0))
    (/ (- mean-return rfree) sd)))