I guess I’m just dense here, but I still don’t see how it can be that the risk adjusted return on capital is unaffected by taxes. Borrowing money (i.e. leverage) adds risk so that can’t be it (or there’s an additional mechanism that comes into play). Later you say that the government is a partner but they aren’t reducing your risk, they’re just taking half your profits.
Probably not worth the back-and-forth more here but to me the “taxes don’t affect returns” position is just obviously wrong and nothing you’ve said shows a mechanism that would change that.
Let’s say the risk-free rate is 0 and the tax rate is 50%. Then 2x leverage doubles your profit and doubles your losses—that’s the sense in which it increases risk. But then taxes cut your profit and losses by the same 50%.
So consider an investment that doubles your money with probability 60%. Without taxes you wanted to invest $X, and have a 60% of making $X and a 40% chance of losing $X. But with a 50% tax rate, you want to invest $2X. Then you have a 60% chance of making $2X, paying half in taxes, and ending up with $X in profit; and a 40% chance of losing $2X, getting half back as a tax rebate, and ending up with $X in losses. So the outcome is identical to the pre-tax world.
Getting back the money immediately, without FUD about whether you’ll ever be able to use the tax rebate, is pretty important to meaningfully reducing your risk. (You also are going to need that rebate in order to pay off the margin loan, and someone is willing to lend it to you precisely because they know that you can use your tax rebate to make them whole if you get wiped out. One reason this may not work in practice is that the person making the margin loan may be concerned about seniority of their debt if they can’t directly claim your tax rebate in the same way a margin lender would traditionally liquidate your assets.)
If the risk-free rate is not zero then the exact same analysis applies---2x leverage multiplies (your return—the risk free rate) by 2, and then a 50% tax rate reduces (your return—the risk free rate) by 2.
I guess I’m just dense here, but I still don’t see how it can be that the risk adjusted return on capital is unaffected by taxes. Borrowing money (i.e. leverage) adds risk so that can’t be it (or there’s an additional mechanism that comes into play). Later you say that the government is a partner but they aren’t reducing your risk, they’re just taking half your profits.
Probably not worth the back-and-forth more here but to me the “taxes don’t affect returns” position is just obviously wrong and nothing you’ve said shows a mechanism that would change that.
Let’s say the risk-free rate is 0 and the tax rate is 50%. Then 2x leverage doubles your profit and doubles your losses—that’s the sense in which it increases risk. But then taxes cut your profit and losses by the same 50%.
So consider an investment that doubles your money with probability 60%. Without taxes you wanted to invest $X, and have a 60% of making $X and a 40% chance of losing $X. But with a 50% tax rate, you want to invest $2X. Then you have a 60% chance of making $2X, paying half in taxes, and ending up with $X in profit; and a 40% chance of losing $2X, getting half back as a tax rebate, and ending up with $X in losses. So the outcome is identical to the pre-tax world.
Getting back the money immediately, without FUD about whether you’ll ever be able to use the tax rebate, is pretty important to meaningfully reducing your risk. (You also are going to need that rebate in order to pay off the margin loan, and someone is willing to lend it to you precisely because they know that you can use your tax rebate to make them whole if you get wiped out. One reason this may not work in practice is that the person making the margin loan may be concerned about seniority of their debt if they can’t directly claim your tax rebate in the same way a margin lender would traditionally liquidate your assets.)
If the risk-free rate is not zero then the exact same analysis applies---2x leverage multiplies (your return—the risk free rate) by 2, and then a 50% tax rate reduces (your return—the risk free rate) by 2.