**Why Look at the Net Present Values And Internal Rates of Return for the 2X-Leveraged ETNs**

The 2X-Leveraged High-Yield ETNs that I follow are still yielding more than 20% on annualized compounded basis. ETNs are exchange-traded notes that have specific maturities. While typically called dividends, the payments from the 2x Leveraged High-Yield ETNs are technically distributions of interest payments on the ETNs, based on the dividends paid by the underlying securities that comprise the index upon which each of them is based, pursuant to the terms of the indentures.

Usually, not much attention is paid to the maturity dates of these ETNs, since the primary reason to buy any of the 2x Leveraged High-Yield ETNs is the high current yield. Many investors are more concerned with the various ways in which the ETNs can be redeemed prior to maturity, rather than when they will mature. Unlike traditional bonds and notes, the principal or face values that a holder will receive at maturity or early redemption of these ETNs, is the net indicative (asset) value of a 2x Leveraged High-Yield ETN, which fluctuates based on the market prices of the components of the index upon which each ETN is based.

The maturity dates of each of the 2x Leveraged High-Yield ETNs are: the UBS ETRACS Monthly Pay 2x Leveraged Closed-End Fund ETN (NYSEARCA:CEFL) due 12/10/2043, the UBS ETRACS Monthly Pay 2x Leveraged Mortgage REIT ETN (NYSEARCA:MORL) due 10/16/2042, the UBS ETRACS Monthly Pay 2X Leveraged Mortgage REIT ETN Series B (MRRL), which is essentially identical in all economic respects to MORL and thus also due 10/16/2042, ETRACS Monthly Pay 2xLeveraged US Small Cap High Dividend ETN (SMHD) due 2/6/2045, UBS ETRACS Monthly Pay 2xLeveraged US Small Cap High Dividend ETN Series B (SMHB) due 11/10/2048, UBS ETRACS 2x Leveraged Long Wells Fargo Business Development Company ETN (NYSEARCA:BDCL) due 5/24/2041, and the Credit Suisse X-Links Monthly Pay 2x Leveraged Mortgage REIT ETN (NYSEARCA: REML) due 7/11/2036.

One reason why not much attention is paid to the various maturity dates which range from 2036 to 2048 is that the payment at maturity is a very small portion of the cash flows that are expected from the 2x Leveraged High-Yield ETNs. That is the case with many ordinary bonds with long maturities. However, it is even more so for the 2x Leveraged High-Yield ETNs. That is especially true when the discounted present values of the cash flows are considered.

The value of any security can be considered the discounted present values of all the future cash flows. The discount factor used to calculate present values is some required rate of return. For an ordinary bond, the discount factor is the market interest rate on bonds of that maturity and credit quality. For an example, for a 30-year bond with a 5% coupon, trading at 100, thus with a 5% yield, the discounted present value of the 100 to be received at maturity is 23.14. If the yield and coupon was 10%, the discounted present value of the 100 to be received at maturity would be only is 5.73. At a yield and coupon of 20%, present value of the 100 to be received at maturity would be only 0.42.

The insignificance of the extremely small portion of the anticipated cash flows for a 2x Leveraged High-Yield ETN accounted for by the principal payment is impacted by another factor. No one can be sure as to what the face value of a 2x Leveraged High-Yield ETN will be on the stated maturity, as the market values of the components in the index will fluctuate. However, it is reasonable to assume that the face value of a 2x Leveraged High-Yield ETN will be expected to decline over time. This is due to the fact that expenses and fees are deducted from the net indicative (asset) value of a 2x Leveraged High-Yield ETN, rather than the income.

The impact of expenses and fees, especially imputed interest expenses, reducing principal rather than income was explained in some of my articles, most recently *Discount To Book Value And 22.6% Yield Make This ETN Attractive,* which included:

.... When considering yields on 2x Leveraged ETNs, such as CEFL, there is another separate factor that could be considered similar to return of capital, that is becoming more significant as the Federal Reserve increases short-term interest rates. An investment in CEFL is functionally the equivalent of buying the 30 high dividend closed-end funds that comprise the index upon which CEFL is based, in a brokerage account using 50% margin. Thus, the value of that hypothetical margin account and the value of CEFL would be expected to move either up or down twice the amount that an unleveraged account holding the same 30 closed-end funds, moved on a percentage basis.

In both the margin account and CEFL, there is interest expense. In the margin account, the brokerage firm charges interest on the margin loan that is used to finance the 50% leverage. In CEFL, there is an imputed interest fee, called a financing expense, that is based on 3-month LIBOR now 2.75%. The financing expense is 3-month LIBOR + 0.40%. This is currently 2.75% + 0.4% = 3.15%.

For most retail investors, the interest on margin loans charged by brokerage firms is far higher than the imputed financing expense in CEFL. For example, Fidelity now charges accounts with less than a margin balance of $25,000, an interest rate of 9.825%. The rate varies with changes in market interest rates and accounts with higher outstanding margin balances pay less on a sliding scale. For accounts with outstanding margin balances over $1,000,000, the current Fidelity rate is 5.50%. TD Ameritrade charges 10.75% on accounts with less than $10,000, charges 10.5% on accounts with $10,000 - $24,999, and 8% on accounts with outstanding margin balances over $1,000,000.

In addition to the interest on margin loans changed by brokerage firms, there would usually be commissions and fees on the transactions associated with buying the 30 high dividend closed-end funds that comprise the index upon which CEFL is based, and possibly rebalancing transactions to maintain the 50% leverage or changes in the index. In addition to the implicit financing expense based on 3-month LIBOR, CEFL has a 0.50% annual tracking fee. In both the margin account and CEFL, the fees and expense reduce the total return to the investor. However, in the margin account, interest expenses and other fees are broken out in the account statement. In funds like YYY, the fees and expenses reduce the income paid in dividends. For 2x Leveraged ETNs, such as CEFL, the interest and tracking fees reduce the net indicative (asset) value.

To the extent that the dividends paid by 2x Leveraged ETNs, such as CEFL, are higher than they would be if the interest and tracking fees were taken from the dividend, the dividend could be considered to include a return of capital. This is separate and distinct from any return of capital associated with some of closed-end funds that comprise the index upon which CEFL is based. This factor was relatively very small when 3-month LIBOR was only 0.25% from 2010 through 2015. However, with 3-month LIBOR now at 2.75%, it is more significant. For example, the CEFL dividend yield on an annualized monthly compounded basis is now 22.6%, based on my projection of the January 2019 CEFL monthly dividend of $0.1744. That calculation is based on a projected annual CEFL dividend of $2.277. Adding the financing expense of 3.15% to the 0.50% annual tracking fee brings total expenses, including interest to 3.65%. If that was taken out of the dividends rather than the net indicative value, the projected annual CEFL dividend would be $1.838 and the annualized monthly compounded basis would be 17.9%. The total return would be the same whether the expense was taken out of principal or income. However, for those who have 2x Leveraged ETNs, such as CEFL, in taxable accounts, you would be paying taxes on higher dividends, that would be the case if the expenses and fees were taken out of the dividends rather than the net indicative value. The lower capital gains or larger capital losses, for tax purposes, from taking the expenses and fees from net indicative value, would usually not offset the higher taxes on the dividends.

The treatment of interest expense is now more significant for 2x Leveraged ETNs, such as CEFL because of the higher short-term interest rates resulting from the tightening by the Federal Reserve. That is not the main reason that the major determinant for the outlook for 2x Leveraged ETNs will be the Federal Reserve's actions. This is discussed in the recent article:

The Federal Reserve Holds The Key To The Outlook For The 2x Leveraged Mortgage REIT ETNs.That article describes how almost all political policy news and economic variables such as unemployment, inflation and growth are now important for the outlook for 2x Leveraged ETNs, mainly to the extent that they can influence decisions and actions by the Federal Reserve. Making the situation even more uncertain, it is not clear how the Federal Reserve would react to a number of specific events. For example, a surge in inflation resulting from increased tariffs could cause the Federal Reserve to be more aggressive in raising rates. Alternately, a surge in inflation resulting from those tariffs could cause the Federal Reserve to consider that surge in inflation to be a one-time event, and not raise rates....

**Calculating Present Values**

When trying to calculate a theoretical present value for a 2x Leveraged ETN, some reasonable estimate of what the net indicative (asset) value could be expected to be at the maturity date is required. Furthermore, even if all interest rates and market values of the components in the index upon which a 2x Leveraged ETN is based were to remain constant, the cash flows would decline as the net indicative (asset) value declined. Some comments on Seeking Alpha have mentioned that the yields on the 2x Leveraged High-Yield ETNs seem to remain relatively stable within a range, while the prices seem to decline on balance. Market fluctuations in the short term overwhelm the gradual reduction in the net indicative (asset) value and thus the market price, due to the impact of expenses and fees reducing principal rather than income. However, over a longer period, the impact of expenses and fees reducing principal becomes significant.

This means that any attempt to calculate a theoretical present value for a 2x Leveraged ETN must adjust both the expected cash flows for each period from income distribution and the expected amount to be paid at the maturity date. A reasonable methodology for reducing the expected cash flows would be to reduce the net indicative (asset) value each period to account for the impact of expenses and fees reducing principal rather than income. Over a long period, even if a 2x Leveraged ETN pays monthly or quarterly, using annual figures has very little impact on the present value calculation.

Present value calculations are used extensively in finance to make investment decisions. When comparing two potential projects, a corporation might pick the one that offers the highest net present value. The net present value is the present value of all future cash flows. Typically, an investment in a project or a security involves a negative cash flow in period 0 when the security or project is paid for and then positive cash flows in subsequent periods.

An investment in a 2x Leveraged ETN involves paying the market price, then receiving periodic cash flows in the form of dividends and a final cash flow at maturity. To calculate the net present value. The negative cash flow in period 0 is subtracted from the sum of the discounted present value of all subsequent positive cash flows. Another way of calculating the present value of 2x Leveraged ETN involves calculating the present value of a growing annuity, which represents the periodic dividend payments and add that to the present value of the final payment. Of course with 2x Leveraged ETNs the "growth rate" in the formula below for a growing annuity negative. Thus, for CEFL we would assume that the net indicative (asset) value and the annual dividend declines by 3.65% each year. Adding the current total financing expense of 3.15% to the 0.50% annual tracking fee brings total expenses, including interest to 3.65%. In the formula below for CEFL using 10% discount factor the first payment would be $2.873, the rate per period would be 10%, the growth rate would be -3.65% and the number of periods would be 24. This simplified model assumes 2019 is period 0 and 2020 is year 1. CEFL matures on 12/10/2043, which is period 24.

It is easier to see and understand the calculation when the present value of each cash flow is calculated separately and then summed. The table I below shows the present value for all of the anticipated cash flows for CEFL. Even though CEFL pays monthly, using annual figures gives a very good approximation. This simplified model assumes 2019 is period 0 and 2020 is year 1. CEFL matures on 12/10/2043. In period 24, the year 2043, not every monthly dividend would actually be paid, and in period 0, the year 2019 some dividends would actually be paid. However, assuming no dividends in 2019 and a full year's dividends in 2043 only understate the net present value slightly.

The January 7, 2019, price of CEFL was $13.23 and the net indicative (asset) value was $13.00. The annualized compounded yield based on the $13.00 net indicative (asset) value, using the most recent three monthly dividends is 22.1%. In year 2019, which is period 0, the only cash flow is the negative $13.23 cost to purchase a share of CEFL. To determine the present value of the future cash flows, for each period the after period 0, the cash flow and net indicative (asset) value is reduced by 3.65%. In 2043, period 24 the cash flow is the sum of the $1.22 dividend and the $5.33 principal payment at maturity. Thus, the period 24 total cash flow is $6.55. The discount factor is 1.0 in period 0 and declines by 10% each period. Thus, in period 1 the net indicative (asset) value is reduced by 3.65% from $13.00 in period 0 to $12.5255. By year 2043, period 24, the discount factor is down to 0.101526. The net indicative (asset) value is reduced to $5.33 and the annual dividend is reduced to $1.22. The discounted present value is determined by multiplying each periods' cash flow by the discount factor.

For period 0 the discount factor is 1.0, so the discounted present value of -$13.23 is -$13.23. For period 24 the discount factor is 0.101526, so the discounted present value of $6.55 is only $0.6647.

Table I CEFL Net Present Value 10% discount factor

dividends | total | discount | discounted | |||

year | period | cash flow | NAV | cash flow | factor | present value |

2019 | 0 | $13 | -13.23 | 1 | -13.23 | |

2020 | 1 | 2.873 | 12.5255 | 2.873 | 0.909091 | 2.611818182 |

2021 | 2 | 2.768136 | 12.06832 | 2.768136 | 0.826446 | 2.287715289 |

2022 | 3 | 2.667099 | 11.62783 | 2.667099 | 0.751315 | 2.003830619 |

2023 | 4 | 2.569749 | 11.20341 | 2.569749 | 0.683013 | 1.755173456 |

2024 | 5 | 2.475954 | 10.79449 | 2.475954 | 0.620921 | 1.537372386 |

2025 | 6 | 2.385581 | 10.40049 | 2.385581 | 0.564474 | 1.346598449 |

2026 | 7 | 2.298508 | 10.02087 | 2.298508 | 0.513158 | 1.179497824 |

2027 | 8 | 2.214612 | 9.655107 | 2.214612 | 0.466507 | 1.033132866 |

2028 | 9 | 2.133779 | 9.302696 | 2.133779 | 0.424098 | 0.90493047 |

2029 | 10 | 2.055896 | 8.963147 | 2.055896 | 0.385543 | 0.792636825 |

2030 | 11 | 1.980856 | 8.635993 | 1.980856 | 0.350494 | 0.694277801 |

2031 | 12 | 1.908554 | 8.320779 | 1.908554 | 0.318631 | 0.608124237 |

2032 | 13 | 1.838892 | 8.01707 | 1.838892 | 0.289664 | 0.532661548 |

2033 | 14 | 1.771773 | 7.724447 | 1.771773 | 0.263331 | 0.466563092 |

2034 | 15 | 1.707103 | 7.442505 | 1.707103 | 0.239392 | 0.408666854 |

2035 | 16 | 1.644794 | 7.170854 | 1.644794 | 0.217629 | 0.357955013 |

2036 | 17 | 1.584759 | 6.909117 | 1.584759 | 0.197845 | 0.31353605 |

2037 | 18 | 1.526915 | 6.656935 | 1.526915 | 0.179859 | 0.274629076 |

2038 | 19 | 1.471183 | 6.413957 | 1.471183 | 0.163508 | 0.240550104 |

2039 | 20 | 1.417484 | 6.179847 | 1.417484 | 0.148644 | 0.210700023 |

2040 | 21 | 1.365746 | 5.954283 | 1.365746 | 0.135131 | 0.184554066 |

2041 | 22 | 1.315896 | 5.736951 | 1.315896 | 0.122846 | 0.161652584 |

2042 | 23 | 1.267866 | 5.527553 | 1.267866 | 0.111678 | 0.141592968 |

2043 | 24 | 1.221589 | 5.325797 | 6.547386 | 0.101526 | 0.664727292 |

Adding all of the discounted present values of the positive cash flows from the dividends and final principal payment results in $20.713. That is the discounted present value of CEFL assuming a 10% required rate of return. Subtracting the present cost to buy CEFL, $13.23 from the $20.713 discounted present values of the positive cash flows, results in a net present value of $7.48.

Corporations use net present value to determine whether or not to make any particular investment. A positive net present value suggests that the investment should be undertaken. A negative net present value suggests that the investment should not be undertaken. For corporations a key issue is what discount factor to use. Generally, corporations use the weighted cost of capital as the discount factor. The cost of debt capital is fairly simple, the after-tax interest rate on the debt. The cost of equity capital is a different, more complex matter. For individual investors the required rate of return could be what securities they would invest in with a similar risk profile if they did not invest in the security in question. Thus could be considered an opportunity cost of investing in one security rather than an alternative security.

The cost of equity capital to a corporation is also the required or expected rate of return to the shareholders of the corporation's equity. The problem is how to calculate the cost of equity capital. One method is to use beta as a measure of risk and plug it in to the formula from the Capital Asset Pricing model:

E(R) = rfr + (beta (E(RM) - rfr))

Where E(R) is the expected rate of return, rfr is the risk-free interest rate, usually assumed to be the rate on US government debt and E(RM) is the expected return on the entire market. All of these variables with the possible exception of the risk-free interest rate are problematic to determine. This is unfortunate since the net present value varies dramatically as the required rate of return and thus the discount factor changes. The table II below shows CEFL Net Present Value using a 5% discount factor.

Table II CEFL Net Present Value 5% discount factor

dividends | total | discount | discounted | |||

year | period | cash flow | NAV | cash flow | factor | present value |

2019 | 0 | $13 | -13.23 | 1 | -13.23 | |

2020 | 1 | 2.873 | 12.5255 | 2.873 | 0.952381 | 2.736190476 |

2021 | 2 | 2.768136 | 12.06832 | 2.768136 | 0.907029 | 2.510780499 |

2022 | 3 | 2.667099 | 11.62783 | 2.667099 | 0.863838 | 2.30394001 |

2023 | 4 | 2.569749 | 11.20341 | 2.569749 | 0.822702 | 2.114139238 |

2024 | 5 | 2.475954 | 10.79449 | 2.475954 | 0.783526 | 1.939974434 |

2025 | 6 | 2.385581 | 10.40049 | 2.385581 | 0.746215 | 1.780157493 |

2026 | 7 | 2.298508 | 10.02087 | 2.298508 | 0.710681 | 1.633506423 |

2027 | 8 | 2.214612 | 9.655107 | 2.214612 | 0.676839 | 1.498936608 |

2028 | 9 | 2.133779 | 9.302696 | 2.133779 | 0.644609 | 1.375452783 |

2029 | 10 | 2.055896 | 8.963147 | 2.055896 | 0.613913 | 1.262141673 |

2030 | 11 | 1.980856 | 8.635993 | 1.980856 | 0.584679 | 1.15816524 |

2031 | 12 | 1.908554 | 8.320779 | 1.908554 | 0.556837 | 1.062754484 |

2032 | 13 | 1.838892 | 8.01707 | 1.838892 | 0.530321 | 0.975203758 |

2033 | 14 | 1.771773 | 7.724447 | 1.771773 | 0.505068 | 0.894865543 |

2034 | 15 | 1.707103 | 7.442505 | 1.707103 | 0.481017 | 0.821145668 |

2035 | 16 | 1.644794 | 7.170854 | 1.644794 | 0.458112 | 0.753498905 |

2036 | 17 | 1.584759 | 6.909117 | 1.584759 | 0.436297 | 0.691424948 |

2037 | 18 | 1.526915 | 6.656935 | 1.526915 | 0.415521 | 0.634464702 |

2038 | 19 | 1.471183 | 6.413957 | 1.471183 | 0.395734 | 0.582196896 |

2039 | 20 | 1.417484 | 6.179847 | 1.417484 | 0.376889 | 0.534234961 |

2040 | 21 | 1.365746 | 5.954283 | 1.365746 | 0.358942 | 0.490224176 |

2041 | 22 | 1.315896 | 5.736951 | 1.315896 | 0.34185 | 0.449839042 |

2042 | 23 | 1.267866 | 5.527553 | 1.267866 | 0.325571 | 0.412780873 |

2043 | 24 | 1.221589 | 5.325797 | 6.547386 | 0.310068 | 2.030134336 |

In this case, the cash flows are all identical to the prior Table I. However, a 5% discount factor increases all of the present values of the future cash flows. Thus, for period 24 the discount factor is 0.310068, so the discounted present value of $6.55 is now $2.03. Adding all of the discounted present values of the positive cash flows from the dividends and final principal payment results in $30.646. That is the discounted present value of CEFL assuming a 5% required rate of return. Subtracting the present cost to buy CEFL, $13.23 from the $30.646 discounted present values of the positive cash flows, results in a net present value of $17.42.

Using a 15% discount factor decreases all of the present values of the future cash flows. The table III below shows CEFL Net Present Value using a 5% discount factor.

Table III CEFL Net Present Value 15% discount factor

dividends | total | discount | discounted | |||

year | period | cash flow | NAV | cash flow | factor | present value |

2019 | 0 | $13 | -13.23 | 1 | -13.23 | |

2020 | 1 | 2.873 | 12.5255 | 2.873 | 0.869565 | 2.49826087 |

2021 | 2 | 2.768136 | 12.06832 | 2.768136 | 0.756144 | 2.093108129 |

2022 | 3 | 2.667099 | 11.62783 | 2.667099 | 0.657516 | 1.753660593 |

2023 | 4 | 2.569749 | 11.20341 | 2.569749 | 0.571753 | 1.469262592 |

2024 | 5 | 2.475954 | 10.79449 | 2.475954 | 0.497177 | 1.230986529 |

2025 | 6 | 2.385581 | 10.40049 | 2.385581 | 0.432328 | 1.031352626 |

2026 | 7 | 2.298508 | 10.02087 | 2.298508 | 0.375937 | 0.864094135 |

2027 | 8 | 2.214612 | 9.655107 | 2.214612 | 0.326902 | 0.723960608 |

2028 | 9 | 2.133779 | 9.302696 | 2.133779 | 0.284262 | 0.606553083 |

2029 | 10 | 2.055896 | 8.963147 | 2.055896 | 0.247185 | 0.508185996 |

2030 | 11 | 1.980856 | 8.635993 | 1.980856 | 0.214943 | 0.425771485 |

2031 | 12 | 1.908554 | 8.320779 | 1.908554 | 0.186907 | 0.356722457 |

2032 | 13 | 1.838892 | 8.01707 | 1.838892 | 0.162528 | 0.29887138 |

2033 | 14 | 1.771773 | 7.724447 | 1.771773 | 0.141329 | 0.250402239 |

2034 | 15 | 1.707103 | 7.442505 | 1.707103 | 0.122894 | 0.209793528 |

2035 | 16 | 1.644794 | 7.170854 | 1.644794 | 0.106865 | 0.175770491 |

2036 | 17 | 1.584759 | 6.909117 | 1.584759 | 0.092926 | 0.147265102 |

2037 | 18 | 1.526915 | 6.656935 | 1.526915 | 0.080805 | 0.123382545 |

2038 | 19 | 1.471183 | 6.413957 | 1.471183 | 0.070265 | 0.103373114 |

2039 | 20 | 1.417484 | 6.179847 | 1.417484 | 0.0611 | 0.086608692 |

2040 | 21 | 1.365746 | 5.954283 | 1.365746 | 0.053131 | 0.072563022 |

2041 | 22 | 1.315896 | 5.736951 | 1.315896 | 0.046201 | 0.060795192 |

2042 | 23 | 1.267866 | 5.527553 | 1.267866 | 0.040174 | 0.050935798 |

2043 | 24 | 1.221589 | 5.325797 | 6.547386 | 0.034934 | 0.228728239 |

For period 24 the discount factor is 0.034934, so the discounted present value of $6.55 is now only $0.2287. Adding all of the discounted present values of the positive cash flows from the dividends and final principal payment results in $30.646. That is the discounted present value of CEFL assuming a 15% required rate of return. Subtracting the present cost to buy CEFL, $13.23 from the $15.37 discounted present values of the positive cash flows, results in a net present value of only $2.14.

**Internal Rates of Return are More Useful for Investors**

Fortunately, for investors there is a way to use discounted present value analysis without having to know any discount factors. As we see from the three CEFL example, changing the discount factor changes the net present value. There is one discount factor that make the net present value equal zero. That is the internal rate of return. For the purpose of our examination of 2x Leveraged High-Yield ETNs, the internal rate of return could be considered the return that an investor would receive after taking into account the expected decline in the net indicative (asset) value and dividends due to the fact that expenses and fees are deducted from the net indicative (asset) value of a 2x Leveraged High-Yield ETN, rather than the income. This assumes neither any improvement or deterioration of market conditions. That is probably as good as any assumption, for the longer term.

For CEFL we get an internal rate of return 17.74%. Table IV shows the results of carrying out the same calculations for the 2x Leveraged High-Yield ETNs that I follow.

Table IV IRR, Present Value with 10% Discount Rate and NPVs for 10%, 5% and 15%

1/7/2019 | indicative | first year | 10% discount | 10% discount | 5% discount | 15% discount | ||||

Price | value | dividends | maturity | IRR | rate PV | rate NPV | rate NPV | rate NPV | ||

CEFL | 13.23 | 13 | 2.87 | 12/10/2043 | 17.74% | $20.71 | $7.48 | $17.42 | $2.14 | |

BDCL | 13.16 | 12.99 | 2.51 | 5/24/2041 | 14.37% | $17.66 | $4.50 | $12.63 | $0.03 | |

MORL | 13.9 | 13.5 | 3.61 | 10/16/2042 | 22.14% | $26.01 | $12.11 | $24.26 | $5.46 | |

MRRL | 13.61 | 13.5 | 3.61 | 10/16/2042 | 22.71% | $26.01 | $12.40 | $24.55 | $5.75 | |

REML | 24.35 | 23.9288 | 6.24 | 7/11/2036 | 21.59% | $42.44 | $18.09 | $34.92 | $8.03 | |

SMHD | 15.72 | 13.78 | 4.20 | 2/6/2045 | 22.63% | $29.35 | $13.63 | $27.39 | $6.21 | |

SMHB | 21.1 | 21.07 | 6.42 | 11/10/2048 | 26.36% | $45.13 | $24.03 | $46.04 | $12.51 |

**Conclusions And Recommendations**

That the net indicative (asset) value and dividends from a 2x Leveraged High-Yield ETN should be expected to decline over time can be a cause of concern or even scary. However, understanding that this is due to the fact that expenses and fees are deducted from the net indicative (asset) value of a 2x Leveraged High-Yield ETN, rather than the income, should alleviate some of the concern.

Deducting the fees and expenses from income rather than principal would not impact the actual returns received from investing in 2x Leveraged High-Yield ETNs. The expected decline over time of the net indicative (asset) value and dividends is a consideration. However, once the magnitude of this factor is understood, it should not be much of an impediment to investing in these 2x Leveraged High-Yield ETNs.

The tables above which give approximate values for the internal rate of returns for these 2x Leveraged High-Yield ETNs assuming markets remain unchanged are not particularly useful for the purposes of prediction, since markets never remain unchanged. However, for the purpose of isolating the impact of the gradual reduction over time in the net indicative (asset) value and dividends from a 2x Leveraged High-Yield ETN, it is a useful assumption.

Investors should consider what other investments that they might make that would have a similar risk as a 2x Leveraged High-Yield ETN, and what the expected return from that alternative investment might be. Quantifying risk is always a problem. The Capital Asset Pricing Model and Modern Portfolio Theory uses beta as a possible measure of risk. Beta is the ratio covariance of an asset's return with the market's return to the variance of the market's return.

An estimate of beta can be obtained with regression analysis of the past returns of an individual security as a function of the return on the overall market. The results of the regression show coefficients including beta. Alpha as in "Seeking Alpha" can also be obtained from such regression analysis. There are many problems associated with beta, including which period to use for the regression and which index should be used to measure the return on the overall market.

Beta for a 2x Leveraged High-Yield ETN could be obtained by using the past returns on the 2x Leveraged High-Yield ETN, or by calculating the betas for each of the components in the index upon which the 2x Leveraged High-Yield ETN is based. The index could be considered a portfolio for which a beta could be estimated. Then the formula for the beta for a leveraged instrument could be applied.

The Capital Asset Pricing Model and Modern Portfolio Theory considers the only risk that investors should be concerned with is systematic risk which is the correlation with the market, since non-systematic risk can be diversified away it is not considered a risk. In that paradigm, the 2x Leveraged High-Yield ETNs would be relatively low risk as their correlations with the entire market is less than many common stocks such as Apple (AAPL). Before you get too excited about the relatively low betas of 2x Leveraged High-Yield ETNs, remember that Powerball lottery tickets have a beta of zero, since their expected returns are completely uncorrelated with the entire market.

The tables above do indicate that the price paid for a 2x Leveraged High-Yield ETN is important. MORL and MRRL are based on the same index. However, the calculated internal rate of return on MRRL is higher because as of the calculation date it was selling for a lower price. The differences in the calculated internal rate of returns on SMHD and SMHB are even more significant even though they are based on the same index. This suggests new investors should focus on which of such pairs are offering the highest internal rate of return at any given time. Additionally, depending on transactions costs some holders of the lower yielding pair may consider selling the one with the lower internal rate of return and using the proceeds to buy the one with the higher internal rate of return. More active traders may want to engage in arbitrage opportunities involving those pairs.

The circumstances and parameters involving possible arbitrage opportunities and how to determine which is the relatively better 2x Leveraged High-Yield ETN to buy at any given set of price points was discussed in my articles: *Sell MORL, Buy MRRL* and *Sell SMHD Yielding 21.5%, Buy SMHB Yielding 23.6%.*

**Disclosure:** I am/we are long BDCL, MRRL, MORL, CEFL, REML, SHMB, SHMD. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.