This is yet another possible arbitrage way to profit, if you are good with Maths, and CAPM short for Capital Asset Pricing Model.
Taking out the expected return which is random, we are have variables for the stocks metrics, in stock price and stock beta or its sensitivity.
Assuming the Law of One Price states that 2 similar assets classes should have the same prices, one could possibly exploit the pricing differences through a number of reasons.
Now let’s say I have yet another pair of stocks called DPO and DDM.
(Taken from Google finance, its description)
DPO:
Dow 30 Enhanced Premium & Income Fund Inc. (the Fund) is a diversified, closed-end management investment company. The investment objectives of the Fund are to provide a high level of premium and dividend income, and the potential for capital appreciation. The Fund pursues its investment objectives principally through a multi-step strategy. The Fund will purchase the 30 common stocks included in the Dow Jones Industrial Average (DJIA Index), weighted in approximately the same proportions as in the DJIA Index (the Dow Stocks). The Fund will also purchase other securities or financial instruments, primarily swap contracts, designed to provide additional investment exposure (leverage) to the return of the Dow Stocks (the Additional Dow Exposure). The Fund also will engage in certain option strategies, primarily consisting of writing (selling) covered call options on some or all of the Dow Stocks (the Options). The Fund’s investment advisor is IQ Investment Advisors LLC.
DDM:
ProShares Ultra Dow30 (the Fund) seeks daily investment results that correspond to twice (200%) the daily performance of the Dow Jones Industrial Average (DJIA). The DJIA is a price-weighted index maintained by editors of The Wall Street Journal. The Index includes 30 large-cap, blue-chip United States stocks, excluding utility and transportation companies. Components are selected through a discretionary process with no predetermined criteria except that components should be established United States companies. The DJIA is not limited to traditionally defined industrial stocks, instead, the Index serves as a measure of the entire United States market, covering such diverse industries as financial services, technology, retail, entertainment and consumer goods. The Fund takes positions in securities and/or financial instruments that, in combination, should have similar daily return characteristics as 200% of the daily return of the Index. Its investment advisor is ProShare Advisors LLC.
Now assuming both the shares track the DJI index or the 30 DJI component stocks, we should achieve the same pricing. But because of the asset value and no. of shares on the open market, they are priced differently.
Lets take a look at how to track them to the similar pricing:
With A as DPO, B as DDM, and only the prices and beta are used here:
A = DPO, $10.24, 0.88
B = DDM, $ 49.28, 1.83
A = (A1 * (1/0.88) = 1.136A1)
B = (B1 * (1/1.83) = 0.54B1)
If A = B (Law of one Price if it exists)
(A1 * (1/0.88) = 1.136A1) = (B1 * (1/1.83) = 0.54B1)
substitute with pricing:
A1 = 10.24
B1 = 49.28
Introducing X and Y to get the proper no. of shares, and multiplying Stock beta with share price:
X(1.136* 10.24) = Y(0.54 * 49.28)
X(11.63264) = Y(26.6112)
11.63264/26.6112 = X/Y
X/Y = 26.6112 / 11.63264
X = 2.28
Y = 1
***
For every 100 share of DDM, we should have 228 shares of DPO to be neutral eg. Long/short or market neutral strategies.
EG:
10.24 * 228 = 2334
49.28 * 100 = 4928
With a 1% movement of DJI, DDM should move 1.83%, while DPO should move 0.88%. But even so, the share value of $2334 and $4928 cannot effective reflect this because:
Even with the right 228 / 100 shares
0.88% x $2334 = $20.53
1.83% x $4928 = $90.18
We need to bring the “Price difference” value to be “equal” or equilibrium.
Taking 90.18 / 20.53 = 4.39
It means the value difference is 4.39 of ratio.
Take 4.39 * 2334 (which is also 228 * 4.39) to bring the “difference” value of DPO closer to DDM.
10.24 * 1000 = 10240
49.28 * 100 = 4928
Now, if DJI moves 1%
0.88% x $10240 = 90.112
1.83% x $4928 = $90.18
So in order to create a “hedge” portfolio, or in finding arbitraging opportunities, we should buy 1000 shares for every 100 shares, at that price of $10.24 and $49.28 respectively. This, unfortunately, only exists in theory, since prices are always fluctuating with demand and supply.
We could use a filter such as Bollinger Bands to filter the upper and lower prices and get the average for the long term instead. One scenario I could think of is this (since DPO regularly gives out huge dividends):
Long DPO, Short DDM
but Long more of DPO instead since the beta is lower and it gives out dividends.
Try at your own risk !
Disclaimer: No positions on above mentioned Stocks
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