What Are "Total Returns?"

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posted

Greetings,

I just created my first algorithm on Quantopian. (Please bear in mind I have no background in stocks and only a little in programming.) The algorithm is probably the dumbest algorithm you could produce. It literally just checks if today's price is higher than yesterday's. If it is, it buys 50 stocks. Otherwise, it does nothing.

yesterday = 0

def initialize(context):  
    context.aapl = sid(24)

def handle_data(context, data):  
    global yesterday  
    today = data[context.aapl].price  
    if today > yesterday:  
        order(context.aapl, 50)  
    else:  
        #order(context.aapl, -50)  
        pass  
    yesterday = data[context.aapl].price

When I run a full backtest, it says my total returns are 836%. How can this be? The algorithm only buys stocks. It doesn't sell them. How exactly is "total returns" computed?

Thanks for taking the time to read this n00b question.

Appreciatively,
—Nathan

8 responses

John Fawcett

Hi Nathan,
Thanks for your question.

If you buy a stock, and the market price of that stock rises, there is a gain in the value. That gain is an unrealized gain because it is in the stock value, not in cash. When you sell the stock you realize the gain. For our simulation and reporting, we show the sum of your realized and unrealized gains as total return. If you are curious about the method of calculating returns over a period, our code for this is open source as the zipline project. The relevant code is in our PerformancePeriod class, which calculates a total value for a portfolio of stocks plus cash at the beginning of a period, and at the end of a period. Period returns are then (end_value - start value) / start_value, which is done in the calculate_performance method.

thanks,
fawce

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Nathan Arthur

Ahh, I see. That makes much more sense. Does that mean a total return of less than 100% would be a loss?

Peter Cawthron

Hello Nathan,

Only a -ve return represents a loss. Also, for you algo to buy all the shares it did you need a starting capital of $12 M which then gives a much more realistic return.

Nathan Arthur

Ok. So my algorithm spent more than my starting capital? What different is happening between using $1m capital and $15m capital? My algorithm's code doesn't take capital into account.

Peter Cawthron

Hello Nathan,

I think the formula for returns is something like:

((Positions Value + Current Cash - Starting Cash) / Starting Cash) *100 %

so with $1 M at the start you have returns of:

((20,260,368 + -10,900,705 - 1,000,000)/1000,000) * 100 = 835.96%

but with $12 M you have returns of:
((20,260,368 + 99,249 - 12,000,000)/12,000,000) * 100 = 69.66%

Something like that, anyway, based on the final 'Positions Value' in a full backtest.

Nathan Arthur

Ahh, yes, looking now I see that I did indeed buy myself into the ground. I'll have to keep in mind that the "Total Returns" value doesn't necessarily reflect debt. Thank you again for the clarification!

John Fawcett

Nathan,

Brokers allow you to borrow capital and stock on margin. When you buy more than your starting capital, you are borrowing money from your broker. Your returns, however, are calculated from your original base. So, if you buy 2x as much stock as your starting base, your returns will be 2x the stock returns. If the stock goes up 5%, your returns would be 10%. If the stock falls 5%, your returns would be -10%. Investing with additional borrowed capital is called using leverage, because of the way it amplifies your (positive or negative) returns.

Whenever you see returns that are extreme, you should immediately be skeptical about the algorithm's management of its leverage.

thanks,
fawce

Disclaimer

Nathan Arthur

I see. That makes sense. So a very confident investor might go into debt in order to take advantage of an opportunity.

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