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If for example I deposit 10,000 dollars in trading account, and I can buy/sell in 20,000, so I'm using leverage.

How returns are computed? I mean that my balance is consist of 20,000 + sum of returns, so what is actually my account value? 10,000 + sum of returns? Thanks guys.

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You have to keep track of both your cash and your stock positions

When you start you have 10,000 in cash, and no stock positions (i.e. zero shares of any stock)

When you buy shares you decrease cash by the purchase cost and you record an increase in the number of shares of that stock. If the cash goes negative it means you are "on margin", i.e. have a margin loan.

When you sell shares you increase cash by the sale proceeds and you decrease the number of shares of stock. If the number of shares goes negative, you are now short.

At any time you can find the market to market value of your account as cash plus the inner product of you share holdings times the current market price of your shares (the long share values are being added and the short shares are being subtracted) $MV=C+p_1 s_1 + \cdots +p_n s_n$

Once a month you earn interest on your cash balance or pay interest on your margin balance (negative cash balance), and this increases or decreases cash.

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  • $\begingroup$ In conclusion, when you have liquidated all your positions and neglecting interest, your statement is correct: the value of the account will be 10,000+sum of profits/losses $\endgroup$
    – nbbo2
    Commented Nov 28, 2017 at 13:26

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