## Effectiveness of considering bandwidth when adapting Moving Average (“MA”) Trading Strategies

Moving average (“MA”) trading strategy is a widely used technical indicator for validating the movement of markets and signaling the buy/sell point.

However, drastic fluctuations in market prices, such as the ones the market experienced last December, 2018; when the market collapsed in a manner of weeks, would lead to a gigantic increase in the incurrence of quantities of trading signals. This in turn, would lead to an increase an enormous jump in the trading cost and also may cause a decrease in the effectiveness of MA Trading Strategies in general.

In order to solve this problem, some experts came up with the concept of bandwidth, the percentage of short-term MA to long-term one when the former surpasses or falls behind the latter. In theory, introducing bandwidth to MA strategies would help filter out some invalid trading signals and improve effectiveness of MA Trading Strategies.

To validate this idea, I started a research by randomly choosing about 50 stocks and collecting the closing prices with the purpose of figuring out the impact of trading signal bandwidth on the effectiveness of MA Trading Strategies.

Through deliberation, I decided to work out the cumulative returns brought by three different strategies, namely buy-and-hold, MA Trading Strategies and MA Trading Strategies considering signal bandwidth.

In order to make the result more considerable, I chose 1 day, 2 days and 5 days as short-term MA, and 20 days, 50 days and 200 days as long-term MA, 0 and 0.01 as the bandwidth. Afterwards, the MA was calculated via:

MA(t.n)=1ni=t-n+1tC(i)

Also, the return of stocks during the holding period was calculated with the formula:

Ctsell and Ctbuy refer to the closing price of the stock on the day it is sold and bought over the holding period respectively. If there are multiple stock holding periods when a trading strategy is adopted, the ultimate cumulative return would be calculated via the following formula:

rcum=i=1n(1+rh,i)

rcum represents the cumulative return and rh,i stands for the return during the i holding period.

Finally, the cumulative returns adopting the three strategies were calculated and compared with each other.

The cumulative return of MA Trading Strategies considering band-width was higher than that of MA Trading Strategies without considering band-width; the cumulative return of MA Trading Strategies without considering band-width was higher than that of buy-and-hold strategies. Hence, bandwidth can actually enhance the effectiveness of MA Trading Strategies.

Written by Xujia Ma & Edited by Alexander Fleiss

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