An analyst is evaluating the average price-to-earnings (P/E) ratio of a portfolio consisting of three stocks. Stock A has a P/E of $10$ and represents $20\%$ of the portfolio's total value. Stock B has a P/E of $15$ and represents $50\%$ of the portfolio's total value. Stock C has a P/E of $25$ and represents $30\%$ of the portfolio's total value. Since P/E is a ratio with earnings in the denominator, what is the portfolio's average P/E ratio calculated using the weighted harmonic mean?