Returns, NAV and drawdowns

NAV is account value: cash plus marked holdings. The simple return between adjacent valuation dates is NAV_t / NAV_(t−1) − 1. A whole-window return may use initial capital instead. Check the starting value before comparing returns.

Drawdown measures the decline from the highest NAV reached so far. With NAV_t / running_peak_NAV − 1, the underwater chart shows zero or negative values. Maximum drawdown is the deepest observed decline in the window; it does not bound future losses.

Check price basis, dividends, fees and observation windows. KabuForge’s jQuantStats view uses N−1 adjacent-NAV intervals and excludes initial capital to the first NAV. The reference TOPIX series is a price index excluding dividends.

NAV moving from 100 to 110 to 99 produces adjacent returns of +10% and −10%. Cumulative return is 99/100−1=−1%; drawdown from the peak of 110 is 99/110−1=−10%. Returns compound rather than simply adding.

Volatility

Volatility usually expresses return variability as a standard deviation. Check sampling frequency, window and annualization. It measures variation, not only losses.

Sharpe ratio

A common form divides mean excess return over a risk-free return by the standard deviation of that excess return, using matching observation frequencies. Check the reference return, costs and sampling frequency. Zero standard deviation makes the ratio unavailable; annualization needs assumptions. See William F. Sharpe’s original discussion for the definition and time dependence.

Benchmark and TOPIX

A benchmark is a reference series for comparison. Price indices differ from dividend-inclusive return indices; this course’s TOPIX series is price-only. Match valuation dates, currencies and treatment of costs and dividends.

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