Take a look at the the debug tools that Quantopian offers when using the IDE environment https://www.quantopian.com/help#debugger. Set breakpoints so you can see what your code is doing.

Anyway, a few things....

1. you have the initialize function defined in three places. Not good. Only define it once. In your app only the last definition ever gets executed.
   
2. 'context.bought' is set to False in the initialize method. In 'handle_data' this variable is checked before executing any trades. Since it is False no trades are ever executed.
   
3. 'context.stock' is set to 'context.portfolio.positions'. When the algorithm starts this is empty. Since you never add any stocks to this list it stays empty and is another reason why your algorithm never buys.

Also, the way you are using the 'data.current' method to get the stock prices, 'current_price' will only contain the last stock price (not the prices of all the stocks). Consider not looping through the stocks (not really very Pythonic anyway) and maybe using a single line something like this. (this method takes either a single stock or a list of stocks as a parameter)

current_prices = data.current(context.stocks, 'price')

You may want to simply place a limit order every day for each of the stocks in your portfolio. This also has the benefit of capturing any intraday dips.

    # Place a limit order at our target 'discount' price for all stocks in our portfolio  
    for stock in context.portfolio.positions:  
        if data.can_trade(stock):  
            limit_price = (1 - DISCOUNT_PERCENT_TO_BUY_AT) * context.portfolio.positions[stock].cost_basis  
            order(stock, 1, style=LimitOrder(limit_price))  

See attached algorithm (note that I set the buy threshold to 2% just to see more trades. set it to 20% in your case)

Dan, thank you for helping me with this.
I tried to backtest this algo but I am having trouble understanding something. Although it is executing purchases (per back test), here are two things I noticed
1: It is not executing at the specified discount. For example, when I set the discount at 10% (0.1), it buys the first share of AAPL at 23.01. The next AAPL purchase is at 21.51. This is a 6.5% drop as opposed to the the specified 10%. In testing it over a long time, there are actually instances where it purchased at a price higher that the cost-basis at that time.

2: It seems the algo is executing only 1 order per stock per day. For example, on a day that AAPL dropped around 7%, the algo made only 1 purchase. After that purchase, the day's price was still more than 10% down from cost basis, but no further order were made for that day.

I am trying to figure of why this is happening but have not succeeded yet.

@Lemuel

1. The 'order' methods default to market orders. They will buy at whatever the next minute price is (after the minute it was entered). Even though there may have been a 10% dip one minute, the next minute after you placed your order the price went up. I'd suggest always entering a limit order. This will guarantee you never pay more than your limit price.

2. Not sure why your algo isn't trading. Maybe attach a backtest?