Timeline for Does financing a portfolio on margin affect the variance of a portfolio?
Current License: CC BY-SA 3.0
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| Jun 16, 2020 at 10:49 | history | edited | CommunityBot |
Commonmark migration
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| Jun 17, 2011 at 23:18 | vote | accept | CommunityBot | moved from User.Id=2654 by developer User.Id=26770 | |
| Jun 17, 2011 at 23:18 | |||||
| Jun 11, 2011 at 20:02 | comment | added | Apoorv | @Havoc, Which is probably @Patience's question I assume. I have edited my answer to reflect the content of our discussion. Thanks for pointing this out! | |
| Jun 11, 2011 at 20:01 | history | edited | Apoorv | CC BY-SA 3.0 |
fixed grammar
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| Jun 11, 2011 at 19:48 | comment | added | Havoc P | Yes, exactly. If we simplify and say market portfolio is S&P500, and risk-free asset is money market fund, then if I have 50% cash 50% S&P500, then I have less variance, if I have 100% S&P500 I have more, and if I have 150% S&P500 with a loan, then I have even more. The amount of my cash or loan doesn't affect the variance of the S&P500 itself (obviously I hope) but it affects the variance of my portfolio (also obviously I hope). So I guess it's a matter of whether the asker wanted to know about leverage affecting variance of S&P500 or variance of their portfolio, in this example. | |
| Jun 11, 2011 at 19:41 | comment | added | Apoorv | @Havoc, So basically it is just dependent upon whether you consider the short to be the part of the book or not. Fair enough. I take back my objections. | |
| Jun 11, 2011 at 19:28 | comment | added | Havoc P | Here is my understanding: the CML shows a range of portfolios with varying leverage; the portfolios each have a different variance (X axis) and expected return (Y axis). The portfolios differ only in degree of leverage. The point of the line is that 1) higher returns and higher risk go hand-in-hand and 2) the "correct" way to increase/decrease both risk and returns is to vary your leverage (positive or negative), rather than deviate from the market portfolio on another dimension, such as changing the weighting of risky assets vs. the market weighting. | |
| Jun 11, 2011 at 19:17 | comment | added | Havoc P | @Monster Truck I would say "leveraged" means your net ownership of the risk-free asset is negative, i.e. you are borrowing money on balance. Just having a loan doesn't mean you are overall leveraged. I agree that a borrowing rate different from risk-free changes CML slope, in fact I just mentioned the same in my answer, but whatever its slope, the variance (on X axis) is higher as you increase leverage. That's the whole point of the line, that as you move along it you get more variance and higher returns. | |
| Jun 11, 2011 at 19:12 | comment | added | Havoc P | i.e. the issue is not the variance of the market portfolio M, the issue is how the variance experienced by the investor changes as they choose less (L) or more (R) leverage, in that graph. That variance changes. | |
| Jun 11, 2011 at 19:12 | comment | added | Apoorv | Hi @Havoc. Borrowing/lending will change the slope of the CML if the borrowing rate is different from the risk free rate (which almost always is the case). Leverage does not increase variance --in fact in the plot I have for CML, variance is the X-axis. Second, how does being leveraged make you own more risky assets? What if I borrow $100 from you to invest in a $100 T-bill? I still have zero market risk (discounting inflation) but I am of course leveraged. I will need to pay you back at whatever rate you lend me but that does not increase the risk because the payment is fixed. | |
| Jun 11, 2011 at 19:07 | vote | accept | CommunityBot | moved from User.Id=2654 by developer User.Id=26770 | |
| Jun 17, 2011 at 23:18 | |||||
| Jun 11, 2011 at 19:00 | comment | added | Havoc P | I'm not sure you have this right. I would say: that equation for variance is how you would compute a variance post-facto after knowing the data points, with a given portfolio. It isn't relevant here. Borrowing or lending does not change the slope of the CML, it's moving you along the CML. As you move along the CML, your expected returns and your variance (or SD) move proportionally together. So all else equal, leverage increases variance (because you own more risky assets). | |
| Jun 11, 2011 at 16:33 | history | answered | Apoorv | CC BY-SA 3.0 |