Question

S&P 500rGSPC) 2,271.31 .62(0.34%) Asof January 20 4:42PM EST. Market closed. S&P 600 (^GSPC) 2,271.31 7.62 (0.34%) As of January 20 4:42PM EST Market closed. l-ー1 쓰 Area . O settings Reset + + compare Area .. O settings +Add Indicator Compare Add Indicator Reset GSPC 2271.31 GSPC 2271.31 open 2269.96 Close 1500 1250 1000 2269.96 2271.31 Low 2265.01 High 227696 Open Closc 2271.31 2271.31 2265.01 2276.96 2.158 13036.55% 500 Vol 2.158 %Chg 13036.55% 96 Chg 1750 1000 2.15G 1961 1975 1989 2003 20 1961 1975 1989 2003

Which plot is the log-scale plot? What does the slope in the log-scale plot mean?

1) Left plot, Log return of S&P500 index

2) Left plot, Change of S&P500 index as a dollar amount

3) Right plot, Log return of S&P500 index

4) Right plot, Change of S&P500 index as a dollar amount

5) None of them, Volatility of S&P500 index

Answer 1

A semi log plot is two dimensional representation of data that uses logarithmic scale on one axis.

In the given plots, second graph uses logarithmic scale to represent the S&P value over time.

Let F(t) be the S&P value at time t.

Hence, we have;

$slope = \frac{(log(F(t_1))-log(F(t_2)))}{t_1-t_2}=\frac{(log(\frac{F(t_1)}{F(t_2)})}{t_1-t_2}$

In semi log slope represents the exponential component of the equation.

Hence, option 4 is the correct option.