Kathy苏苏 · 2023年02月19日
NO.PZ2020021205000026
问题如下：
Monthly stock prices are as follows in USD: 35, 38, 41, 37, 33, and 32. Use this data to estimate the volatility per year.
选项：
解释：
The calculations are in the following table. In this case, the average value of the u; is -0.01792 and = 0.03711 and the standard deviation of the u; is = 0.0942
so that the volatility is 0.0942 = 0.326 or 32.6%.
estimate the volatility per year是求return的volatility是吗？怎么看出是return的volatility，而不是price的volatility呢？谢谢。
pzqa27 · 2023年02月20日
嗨，爱思考的PZer你好：
这个问题问的好，这需要有一些金融思维常识。这里是算return的波动，原因很简单。因为股价的波动率是没有意义的。比如贵州茅台一股的价格是2000元左右，招商银行的股价在几十元。这俩股票分别算个波动率，是没法放一起比较的，因为数量级就不一样，因此正常做金融投资时，一般都是对回报率进行建模，没人对股价进行建模，所以求波动也是一般求回报率的波动，而不是股价的波动，因为股价没有研究的意义
----------------------------------------------就算太阳没有迎着我们而来，我们正在朝着它而去，加油！
NO.PZ2020021205000026问题如下Monthly stoprices are follows in US 35, 38, 41, 37, 33, an32. Use this ta to estimate the volatility per year.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #454046}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #464045}span.s1 {color: #6b5147}span.s2 {color: #4b5a6e}span.s3 {color: #303c63}The calculations are in the following table. In this case, the average value of the u; is -0.01792 an∑i=15ui2\sum_{i=1}^5ui^2∑i=15ui2= 0.03711 anthe stanrviation of the u; is 14(0.03711 − 5 X 0.017922)\sqrt{\frac14(0.03711\;-\;5\;X\;0.01792^2)}41(0.03711−5X0.017922)= 0.0942 so ththe volatility is 0.094212\sqrt{12}12 = 0.326 or 32.6%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f46}span.s1 {color: #777777}span.s2 {color: #466b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474047}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4b434b}span.s1 {color: #303b5f}span.s2 {color: #4b586c}span.s3 {color: #6b5347}span.s4 {color: #303c63}span.s5 {font: 5.0px Helvetica}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474348}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4135}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #473f46}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f47}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464550}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #45434b}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #524c4e}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464750}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454047}span.s1 {color: #777777}span.s2 {color: #635e60}span.s3 {color: #4b5a6e}span.s4 {font: 5.0px Helveticcolor: #635e60}span.s5 {font: 5.0px Helvetica}span.s6 {color: #636b73}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464045}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453e42}span.s1 {color: #4b5a6e}span.s2 {color: #6b5547}span.s3 {color: #303b5f}span.s4 {color: #5f544f}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #433e44}span.s1 {color: #757575}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}span.s1 {color: #6b5147}span.s2 {color: #303b5f}span.s3 {color: #466b}span.s4 {color: #777373}1、红色表述是不是错了？按照红色线是写成这样的2、1/4和5是什么意思？看了往期解答也不明白3、求年的波动率要用样本方差而不是总体方差？4、0.007097是总体方差，0.084246是样本标准差？不明白，为什么样本直接求出来的居然是总体值？5、若0.007097是总体方差，用它除以（5-1）再开跟号，结果是0.042122，哪里算错了呢？
NO.PZ2020021205000026问题如下Monthly stoprices are follows in US 35, 38, 41, 37, 33, an32. Use this ta to estimate the volatility per year.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #454046}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #464045}span.s1 {color: #6b5147}span.s2 {color: #4b5a6e}span.s3 {color: #303c63}The calculations are in the following table. In this case, the average value of the u; is -0.01792 an∑i=15ui2\sum_{i=1}^5ui^2∑i=15ui2= 0.03711 anthe stanrviation of the u; is 14(0.03711 − 5 X 0.017922)\sqrt{\frac14(0.03711\;-\;5\;X\;0.01792^2)}41(0.03711−5X0.017922)= 0.0942 so ththe volatility is 0.094212\sqrt{12}12 = 0.326 or 32.6%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f46}span.s1 {color: #777777}span.s2 {color: #466b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474047}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4b434b}span.s1 {color: #303b5f}span.s2 {color: #4b586c}span.s3 {color: #6b5347}span.s4 {color: #303c63}span.s5 {font: 5.0px Helvetica}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474348}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4135}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #473f46}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f47}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464550}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #45434b}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #524c4e}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464750}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454047}span.s1 {color: #777777}span.s2 {color: #635e60}span.s3 {color: #4b5a6e}span.s4 {font: 5.0px Helveticcolor: #635e60}span.s5 {font: 5.0px Helvetica}span.s6 {color: #636b73}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464045}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453e42}span.s1 {color: #4b5a6e}span.s2 {color: #6b5547}span.s3 {color: #303b5f}span.s4 {color: #5f544f}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #433e44}span.s1 {color: #757575}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}span.s1 {color: #6b5147}span.s2 {color: #303b5f}span.s3 {color: #466b}span.s4 {color: #777373}红色框是怎么计算的呢？ln1.0857是2.6哦？样本方差是怎么酸的？
NO.PZ2020021205000026问题如下Monthly stoprices are follows in US 35, 38, 41, 37, 33, an32. Use this ta to estimate the volatility per year.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #454046}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #464045}span.s1 {color: #6b5147}span.s2 {color: #4b5a6e}span.s3 {color: #303c63}The calculations are in the following table. In this case, the average value of the u; is -0.01792 an∑i=15ui2\sum_{i=1}^5ui^2∑i=15ui2= 0.03711 anthe stanrviation of the u; is 14(0.03711 − 5 X 0.017922)\sqrt{\frac14(0.03711\;-\;5\;X\;0.01792^2)}41(0.03711−5X0.017922)= 0.0942 so ththe volatility is 0.094212\sqrt{12}12 = 0.326 or 32.6%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f46}span.s1 {color: #777777}span.s2 {color: #466b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474047}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4b434b}span.s1 {color: #303b5f}span.s2 {color: #4b586c}span.s3 {color: #6b5347}span.s4 {color: #303c63}span.s5 {font: 5.0px Helvetica}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474348}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4135}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #473f46}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f47}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464550}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #45434b}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #524c4e}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464750}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454047}span.s1 {color: #777777}span.s2 {color: #635e60}span.s3 {color: #4b5a6e}span.s4 {font: 5.0px Helveticcolor: #635e60}span.s5 {font: 5.0px Helvetica}span.s6 {color: #636b73}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464045}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453e42}span.s1 {color: #4b5a6e}span.s2 {color: #6b5547}span.s3 {color: #303b5f}span.s4 {color: #5f544f}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #433e44}span.s1 {color: #757575}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}span.s1 {color: #6b5147}span.s2 {color: #303b5f}span.s3 {color: #466b}span.s4 {color: #777373}标准差那个公示没理解，为啥直接是5收益平方和-5均值，感觉少了很多
NO.PZ2020021205000026 问题如下 Monthly stoprices are follows in US 35, 38, 41, 37, 33, an32. Use this ta to estimate the volatility per year.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #454046}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #464045}span.s1 {color: #6b5147}span.s2 {color: #4b5a6e}span.s3 {color: #303c63} The calculations are in the following table. In this case, the average value of the u; is -0.01792 an∑i=15ui2\sum_{i=1}^5ui^2∑i=15ui2= 0.03711 anthe stanrviation of the u; is 14(0.03711 − 5 X 0.017922)\sqrt{\frac14(0.03711\;-\;5\;X\;0.01792^2)}41(0.03711−5X0.017922)= 0.0942 so ththe volatility is 0.094212\sqrt{12}12 = 0.326 or 32.6%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f46}span.s1 {color: #777777}span.s2 {color: #466b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474047}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4b434b}span.s1 {color: #303b5f}span.s2 {color: #4b586c}span.s3 {color: #6b5347}span.s4 {color: #303c63}span.s5 {font: 5.0px Helvetica}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474348}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4135}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #473f46}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f47}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464550}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #45434b}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #524c4e}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464750}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454047}span.s1 {color: #777777}span.s2 {color: #635e60}span.s3 {color: #4b5a6e}span.s4 {font: 5.0px Helveticcolor: #635e60}span.s5 {font: 5.0px Helvetica}span.s6 {color: #636b73}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464045}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453e42}span.s1 {color: #4b5a6e}span.s2 {color: #6b5547}span.s3 {color: #303b5f}span.s4 {color: #5f544f}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #433e44}span.s1 {color: #757575}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}span.s1 {color: #6b5147}span.s2 {color: #303b5f}span.s3 {color: #466b}span.s4 {color: #777373} 题目中给的条件是股价stoprice的样本，讲解答案显示先计算Ln(si/si-1)的均值，这是收益率均值，依据收益率均值计算的是收益率的the volatility per year，不是股价的the volatility per year。是这样的吗？看题目表述，感觉是求股价的波动，不是吗？遇到这类题目，在怎么区分是求股价的波动，还是求收益率的波动呢？谢谢老师
NO.PZ2020021205000026问题如下 Monthly stoprices are follows in US 35, 38, 41, 37, 33, an32. Use this ta to estimate the volatility per year.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #454046}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.0px Helveticcolor: #464045}span.s1 {color: #6b5147}span.s2 {color: #4b5a6e}span.s3 {color: #303c63}The calculations are in the following table. In this case, the average value of the u; is -0.01792 an∑i=15ui2\sum_{i=1}^5ui^2∑i=15ui2= 0.03711 anthe stanrviation of the u; is 14(0.03711 − 5 X 0.017922)\sqrt{\frac14(0.03711\;-\;5\;X\;0.01792^2)}41(0.03711−5X0.017922)= 0.0942 so ththe volatility is 0.094212\sqrt{12}12 = 0.326 or 32.6%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f46}span.s1 {color: #777777}span.s2 {color: #466b}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474047}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4b434b}span.s1 {color: #303b5f}span.s2 {color: #4b586c}span.s3 {color: #6b5347}span.s4 {color: #303c63}span.s5 {font: 5.0px Helvetica}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #474348}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #4135}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #473f46}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453f47}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464550}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #45434b}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #524c4e}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464750}p.p10 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454047}span.s1 {color: #777777}span.s2 {color: #635e60}span.s3 {color: #4b5a6e}span.s4 {font: 5.0px Helveticcolor: #635e60}span.s5 {font: 5.0px Helvetica}span.s6 {color: #636b73}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #464045}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #453e42}span.s1 {color: #4b5a6e}span.s2 {color: #6b5547}span.s3 {color: #303b5f}span.s4 {color: #5f544f}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #433e44}span.s1 {color: #757575}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.0px Helveticcolor: #454048}span.s1 {color: #6b5147}span.s2 {color: #303b5f}span.s3 {color: #466b}span.s4 {color: #777373}同学您好，样本方差是 [ (各个X的平方和) - (均值的平方*n) ] / (n-1)老师看到您给其他同学回复的有上面那个公式，我想问一下这个公式是在哪个位置讲的，因为没有印象有这个公式，谢谢老师！
