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Now that ETRACS Monthly Pay 2xLeveraged Mortgage REIT ETN (NYSEARCA:MORL) is yielding about 30%, it seems like a good time to revisit classic risk and return theory and see how it might apply here. MORL and Market Vectors Mortgage REIT ETF (NYSEARCA:MORT) are baskets of 25 mREITS. They comprise a little universe that may allow us to utilize and test the concepts of risk and return embodied in Modern Portfolio Theory.

Anyone who has taken a graduate finance course and many others are familiar with the work of Markowitz which led to of Modern Portfolio Theory. This led to the Capital Asset Pricing Model and Jensen's alpha which is the Alpha in "Seeking Alpha." The basis for the theory is that investors evaluate all assets in terms of expected return and risk. Risk can be quantified by standard deviation. Any asset is more efficient than another asset if it has a higher expected return than the other asset but no more risk, or has the same expected return but less risk.

http://en.wikipedia.org/wiki/File:Markowitz_frontier.jpg

If all possible assets and portfolios of assets are plotted on a graph with expected return on the vertical axis and risk on the horizontal assets as, shown above, there will be some assets and portfolios of assets that are more efficient than others.

The most efficient assets and portfolios of assets, those which have the highest expected return for any given level of risk (standard deviation) form the Efficient Frontier. This, as shown above, is the line connecting those assets and portfolios of assets that are more efficient than those below then in terms of risk and return.

Portfolios of assets will generally be more efficient than individual assets. Compare investing all of your money in one security that had an expected return of 10% with some level of risk, to a portfolio comprised of 20 securities each with an expected return of 10% with same level of risk as the single security. The portfolio would provide the exact same expected return of 10% but with less risk than the individual security. Thus, the portfolio is more efficient than any of the individual assets in the portfolio.

This principle of diversification has the to the boom in index funds and ETFs. Markowitz demonstrated that the most efficient portfolio will be the Market Portfolio, which consists of all assets that anyone could invest in. That would include not just all domestic and international stocks and bond but all other assets as well including art and collectibles such as baseball cards. In a model where a risk free interest rate exists at which all investors can borrow and lend, all investors should own the Market Portfolio, as the line labeled "Best possible CAL" on the graph indicates. The best possible capital asset allocation for any investor, regardless of risk preferences, lies along a line that connects the risk free rate with the Efficient Frontier. The risk or standard deviation of an investment at the risk free rate is zero. A line originating at the point of the risk free interest rate on the Expected return vertical axis and zero on the Standard Deviation axis can be drawn to tangency point on the Efficient Frontier. Any investor should invest at some point on that Best possible CAL. An extremely risk averse investor should invest only in the risk free asset. Someone slightly less risk averse should have most of their assets in the risk free asset with the remainder in the market portfolio. A risk seeking investor could have 200% of their assets in the Market portfolio by buying on margin by borrowing at the risk free rate.

The important implication is that any point on the Best possible CAL is more efficient than any individual asset or portfolio below that point, since it has a higher return with the same risk. Modern Portfolio Theory has had its ups and downs in both the financial and academic communities. Critics of the theory and model point to the difficulty in determining or creating a "market portfolio" and the assumption that investors can borrow and lend at a risk free rate. Many use the S&P 500 as a proxy for the market portfolio and the t-bill rate as the risk free rate. There still remain numerous issues with the model. One could argue that the Wilshire 5000 is a better proxy than the S&P 500.

One way of applying and testing Modern Portfolio Theory is to consider only the relatively small universe of mREITS. In particular the 25 mREITS that comprise MORT which can be seen at: vaneck.com/market-vectors/income-etfs/mo.../

All Fund Holdings as of 06/21/2013

Number

Holding

Ticker

Shares

Market Value

% of net assets

1

Annaly Capital M

NLY US

1,308,003

$16,559,317.98

15.42%

2

American Capital Agency Corp

AGNC US

552,966

$12,955,993.38

12.07%

3

Chimera Investment Corp

CIM US

2,035,600

$5,943,952.00

5.54%

4

Mfa Financial Inc

MFA US

685,908

$5,631,304.68

5.24%

5

Hatteras Financial Corp

HTS US

213,589

$5,361,083.90

4.99%

6

Starwood Property Trust Inc

STWD US

227,401

$5,318,909.39

4.95%

7

Two Harbors Investment Corp

TWO US

485,412

$5,257,011.96

4.90%

8

Invesco Mortgage Capital

IVR US

274,895

$4,862,892.55

4.53%

9

Northstar Realty Finance Cor

NRF US

528,622

$4,509,145.66

4.20%

10

Cypress Sharpridge Investmen

CYS US

462,118

$4,473,302.24

4.17%

11

Armour Residential Reit Inc

ARR US

847,661

$3,913,499.17

3.65%

12

Redwood Trust Inc

RWT US

213,634

$3,799,969.20

3.54%

13

New Residential Investment

NRZ US

515,832

$3,376,922.44

3.15%

14

Colony Financial Inc

CLNY US

168,908

$3,357,891.04

3.13%

15

Capstead Mortgage Corp

CMO US

249,817

$3,095,232.63

2.88%

16

Pennymac Mortgage Investment

PMT US

144,610

$2,905,214.90

2.71%

17

American Capital Mortgage In

MTGE US

155,786

$2,896,061.74

2.70%

18

Newcastle Investment Corp

NCT US

515,832

$2,662,535.48

2.48%

19

Istar Financial Inc

SFI US

199,327

$2,188,610.46

2.04%

20

Anworth Mortgage Asset Corp

ANH US

377,575

$2,125,747.25

1.98%

21

Resource Capital Corp

RSO US

255,156

$1,581,967.20

1.47%

22

Apollo Commercial Real Estate

ARI US

89,495

$1,451,608.90

1.35%

23

Dynex Capital Inc

DX US

134,672

$1,375,001.12

1.28%

24

Rait Financial Trust

RAS US

159,194

$1,193,955.00

1.11%

25

Winthrop Realty Trust

FUR US

77,697

$911,385.81

0.85%

If we restrict ourselves to the mREIT universe we can use MORT as a very good proxy for the market portfolio. The issue of borrowing and lending at a risk free rate remains. Any investor can lend at close to the risk free rate via instruments such as t-bills, certificates of deposit or money market accounts. Borrowing at the risk free rate is another matter. Certainly large investors financial institutions can borrow close to risk free rate. However, individual retail investors usually cannot. Margin rates at Schwab, for example, start at 8.5% on balances up to $25,000 with 6.0% being the lowest rate available for balances above $2.5 million.

The Modern Portfolio Theory works pretty well for risk averse investors in the mREIT universe. Someone who wanted less risk than buying a single mREIT could buy a portfolio of 25 mREITs approximated weighted by market capitalization or buy MORT. If they wanted half the risk of owning MORT, they could keep half of their money a risk free investment and half in MORT. Of course, they would have to accept the lower return that comes with the reduced risk.

For a retail investor willing to accept more risk and seeking higher returns buying individual mREITs or MORT on margin, borrowing at close to the risk free rate may not be possible. An investor who had $50,000 in their account and used margin to buy $100,000 of MORT would be doubling the risk but not increasing the expected return in an efficient way. With the SEC yield on MORT at 11.74%, paying 7% on the funds used to buy the extra $50,000 of MORL would make the return on the account 16.48%. However, if the investor could pay .4% on borrowing, as large investors and institutions can, the return on the account would be 23.08%.

For a retail investor willing to accept more risk and seeking higher returns buying MORL, as opposed to buying MORT on margin, is much more efficient. MORT has only been trading since October 17, 2012, the daily standard deviation of returns since then has been 2.33%. That is about twice the daily standard deviation of returns for MORL which was 1.15% for the same period. That is exactly what would be expected since MORL is essentially the portfolio of MORT leveraged 2X. However, MORL borrows from its sponsor UBS at .4%.

MORL does not publish an SEC yield. However, if it did it would be very close to slightly less than twice that of MORT. MORT pays a monthly dividend that varies greatly per month since most of the mREITs in the basket pay dividends quarterly on various different schedules. During any three month period all of the components would have paid their dividends. The last three dividends paid by MORL were: $0.116 in June, $0.126 in May and $1.321 in April. That is a quarterly rate of $1.563 and an annual rate of $6.252. At a price of $20.75 that is a yield more than 30%. The two largest components of MORL, Annaly Capital (NYSE:NLY) and American Capital Agency Corp. (NASDAQ:AGNC) have recently cut their dividends. Thus, MORL's future dividends will be somewhat less, most likely yielding slightly less than twice that of MORT.

MORL pays dividends monthly. Many investors are not aware of how much the effect of monthly compounding can be at high yields. A simple 30% annual yield becomes effective 34.48% when compounded monthly. That the monthly dividends vary by amount each month does not affect the math in terms of the effect of compounding. The difference between a simple 30% and the effective compounded rate is greater than the current rate on 30-year treasury bonds.

I calculated the standard deviation for each of the components of MORT and MORL for the period since MORL began trading. The standard deviation of daily returns for MORT was less than that of any of the components and the standard deviation of daily returns for MORL was greater than that of any of the components. There was not enough trading data for New Residential Investment (NYSE:NRZ) to calculate standard deviations for the comparable period.

When considering the risk reduction obtainable from using a portfolio instrument as opposed to individual assets, the correlation between the individual assets and the portfolio instrument must be considered. If all of the individual components were perfectly correlated with MORL or MORT, then they would provided no diversification. However, as long as the correlation is not perfect, there is some benefit.

I ran regressions of the returns on each of the components as a function of the return on MORT over the period since October 17, 2012. The extent that the variation in each of the components depends upon MORT is quantified by the coefficient of determination, denoted R2, a value of 1.0 means that the individual mREIT would move exactly in lockstep with MORT. A value of 0.0 would mean they are totally unrelated.

Not all of the mREITs that comprise the index that MORL and MORT are based upon are highly correlated with the index. That is because of some specific aspects of the individual mREITS. As would be expected NLY and AGNC had relatively high R2 since they have large weights in the index. Other mREITS that also borrow short-term to buy agency securities such as Invesco Mortgage Capital (NYSE:IVR), Cypress Sharpridge (NYSE:CYS) and Armour Residential Reit Inc (NYSE:ARR) have high R2. This is because they are also sensitive to possible changes in short-term rates that could affect their financing costs. Chimera Investment Corp (NYSE:CIM) has a low R2 since during that period its price was highly influenced by the issue of whether or not it would be filing its 10-K forms on time. Rait Financial Trust (NYSE:RAS) and Winthrop Realty Trust (NYSE:FUR) have very low R2 since a significant portion of their assets are actual real estate. Thus, the economic conditions which a associated with lower interests rates, such as high unemployment, which would be good for agency mREITS could be bad for those who own actual real estate.

Stnd Dev

R2

MORL

2.33

MORT

1.15

Annaly Capital M

NLY US

1.27

0.74

American Capital Agency Corp

AGNC US

1.58

0.71

Chimera Investment Corp

CIM US

1.63

0.35

Mfa Financial Inc

MFA US

1.11

0.66

Hatteras Financial Corp

HTS US

1.15

0.68

Starwood Property Trust Inc

STWD US

1.31

0.44

Two Harbors Investment Corp

TWO US

1.73

0.49

Invesco Mortgage Capital

IVR US

1.56

0.73

Northstar Realty Finance Cor

NRF US

1.9

0.47

Cypress Sharpridge Investmen

CYS US

1.49

0.68

Armour Residential Reit Inc

ARR US

1.69

0.67

Redwood Trust Inc

RWT US

1.71

0.38

New Residential Investment

NRZ US

only since 5/2/13

Colony Financial Inc

CLNY US

1.37

0.39

Capstead Mortgage Corp

CMO US

1.22

0.7

Pennymac Mortgage Investment

PMT US

1.7

0.56

American Capital Mortgage In

MTGE US

1.51

0.57

Newcastle Investment Corp

NCT US

2.18

0.48

Istar Financial Inc

SFI US

1.99

0.31

Anworth Mortgage Asset Corp

ANH US

1.16

0.64

Resource Capital Corp

RSO US

1.36

0.47

Apollo Commercial Real Estat

ARI US

1.21

0.49

Dynex Capital Inc

DX US

1.2

0.64

Rait Financial Trust

RAS US

2.18

0.17

Winthrop Realty Trust

FUR US

1.2

0.17

As the table above shows, MORT and MORL provide a surprisingly high degree of diversification within the universe of mREITS. This is due to the fact that systematic macro events such as changes in unemployment and inflation rates have disparate effects of the various components in the index. This implies that the risk and return parameters appear favorable in terms of MORL providing a efficient instrument for those seeking higher yields.

Source: 30% Yielding MORL, MORT And The mREITS: A Real World Application And Test Of Modern Portfolio Theory