A New Narrative on Asset Allocation

How does AlphaSimplex use futures contracts to implement its strategies?

Given the volatility in the markets over the past few years, the need to manage risk allocation has become more crucial for investors. The volatility of volatility can change rapidly and this would be reflected in the VIX. Andrew Lo, MIT professor and alternative money manager, mentions that in the investing arena, there are new rules to abide by. The first is that markets are not stable and you cannot be reasonably assured of the volatility in your traditional 60% stock / 40% bond portfolio. The second rule is that while most people think they are well diversified amongst different asset classes, it is not true. There is a need to diversify across stocks, bonds, currencies, commodities and interest rates. The third rule is that we have to be aware that while stocks provide good returns in the long run, we are dead in the long run. Hence we have to be able to manage the short term swings.

These rules lead to the new narrative that we cannot allocate funds to asset classes without looking at their associated volatility. AlphaSimplex seeks to cater to the need for risk allocation for portfolios. The fund takes an approach where they establish a volatility goal, for example 8%. They invest in futures contracts across a variety of asset classes in order to maintain that level of volatility. They rebalance on a daily basis. For example, if the volatility of the underlying asset spikes, the fund will reduce exposure in that asset class via futures. When the volatility subsides, the fund will increase exposure in that asset class via futures. The act of managing this volatility on a daily basis is something that individual investors would have a difficult time replicating. The fund has established a goal of 8% volatility.

This method of risk allocation comes in contrast to the traditional asset allocation approach, which does not account for wild swings in volatility which have been omnipresent over the past 4-5 years. 

Lo discusses that it would be difficult for an individual investor to replicate this sort of daily rebalancing. However, he mentions that investors should still be knowledgeable about correlations amongst asset classes and cognizant of risk not only when markets are volatile but also during calmer periods.  

Debtco's Debt Debate

This week we are looking at different pricing methods for securities. In this case company Debtco has a total enterprise value (1) of $100 million and has issued zero-coupon bonds with an aggregate face value of $80 million (80,000 bonds each with a face value of $1,000) with a one-year maturity date.  The risk free interest rate is 8% and the volatility of the firms’ assets are 30%. Using the Black-Scholes model:

and substituting the call option for Debtco’s equity and the exercise price for the face value of Debtco’s debt, we can use the following formula to find the value of Debtco’s equity:

V= 100

B = 80

T = 1

SD = 0.3

Using this formula we find the value of equity is $28.24 million, making the value of debt (D) worth $71.86 million. Because Debtco issued zero-coupon, one year bonds

the yield-to-maturity will equal the promised rate of interest (R), found in this formula:

The YTM equals: (ln(80/71.86))/1 = 10.87%

This computation can also be done in excel using the options valuing spread-sheet provided at www.mhhe.com/bkm

INPUTS			OUTPUTS
Standard Deviation	0.3		d1	1.1605
Maturity (in years)	1		d2	0.8605
Risk-free rate	0.08		n(d1)	0.8771
Value of Firm	100		N(d2)	0.8052
Bond Value	80		Equity Value	28.2411
Dividend Yield	0		B/S put value	2.0904
Value of Debt	71.7589
YTM	10.87%

The aggregate face value of Debtco’s bond increased to $108.33 million. Using the same formula, the new YTM on Debtco’s debt is 20.70%.

INPUTS			OUTPUTS
Standard Deviation	0.3		d1	0.1500
Maturity (in years)	1		d2	-0.1500
Risk-free rate	0.08		n(d1)	0.5596
Value of Firm	100		N(d2)	0.4404
Bond Value	108.33		Equity Value	11.9230
Dividend Yield	0		B/S put value	11.9242
Value of Debt	88.0770
YTM	20.70%

Assume that the firm's management swaps its assets for riskier assets of the same total value.  How would this asset swap affect the value of its debt and equity?  Explain

Later, Debtco decides to swap its assets for riskier assets of the same total value (100 million). When the volatility of Debtco’s assets increases, the value of the equity must increase to offset lower value of the the debt due to uncertainty in repayment  (lower value, higher yields).

 In the below example, the face value of debt is 80 million and the total value is 100 million, the volatility has increased to 50%. We find that the value of equity has increased to 33.2 million and the value of debt has decreased to 66.8 million. The YTM on the debt has increased to 18.04%. 

INPUTS			OUTPUTS
Standard Deviation	0.5		d1	0.8563
Maturity (in years)	1		d2	0.3563
Risk-free rate	0.08		n(d1)	0.8041
Value of Firm	100		N(d2)	0.6392
Bond Value	80		Equity Value	33.2045
Dividend Yield	0		B/S put value	7.0538
Value of Debt	66.7955
YTM	18.04%

(1) TEV = Market Capitalization + Interest Bearing Debt + Preferred Stock - Excess Cash

Hartford to Buy Out Annuities

The Hartford just announced to investors and analysts that they are seeking regulatory approval to make offers to a small number of annuity owners to swap the income guarantees on their contracts for boosts to the amounts that they have invested in underlying stock and bond funds.

A variable annuity is an insurance contract that delays payment of income until the investor chooses to receive them. There are typically two phases: a savings phase and an income phase. Earnings within the contract are tax deferred until withdrawal, similar to a 401K plan. Similar to a 401K plan, there is a 10% early withdrawal penalty if funds are taken out before the age of 59 and 1/2. If an annuity is held within a retirement plan, it is considered a "qualified" annuity and distributions are completely taxable. If held outside of a retirement plan, it is known as "non-qualified" and only earnings are taxed. Withdrawals are made on a earnings first, basis last principle. Variable annuities come with an assortment of insurance options, all of which add to the cost of investment in the contract.

The basic insurance benefit associated with variable annuities is the death benefit. It assures the beneficiaries of the annuity guaranteed payment if the contract owner dies before annuitizing the contract. There are several options for this, each with different costs associated with it.

Among the living benefits, which include annuitizing your investment to receive guaranteed minimum income, the benefit to discuss here is the Guaranteed Lifetime Withdrawal Benefit (GLWB), which does not require annuitizing, and therefore handing over control, of your investment. The guarantee is a set percentage of your investment, which increases the longer you delay payment. The company may agree to pay you 5% at age 55, but might increase it to 5.5% or 6% if you wait until age 70 or 80. Coupled with death benefits, insurance companies make money off these contracts based on the underlying fees charged to clients because they don't get to keep the account balance like an annuitized contract e.g. an immediate annuity.

The Hartford is seeking permission to ask variable annuity owners to give up their guarantee of lifetime income probably because the projections on how the market would perform, which the guarantees the Hartford were giving as part of their VA products were based, were way off. A lot of analysts were expecting a correction of some sort but very few thought we'd have the magnitude of a recession like we did in 2008-2009. Even with hedging programs in place, it's difficult to maintain a level of guaranteed payment to investors under contract until they die (defined benefit plans, anyone?).

The Hartford is offering a boost to the amount of money in accounts held by owners of these contracts in exchange for canceling the guaranteed lifetime withdrawal.

The people who would most likely benefit from accepting this offer are people who are close to death and the expected value of the future guaranteed payments are less than the boost the Hartford is offering. It is likely by this stage, surrender charges have disappeared and they can try to roll over this account into a traditional mutual fund company in similar investments and save on fees.

The people who are worse off accepting this offer are those that are expected to take the guaranteed withdrawals for decades in retirement and the expected value of these future payments outweigh the boost the Hartford is offering.

Honda Analysis

15.

In the first scenario where the PV of CF is 39.71, let’s make note that ROE is greater than cost of equity. If this relationship holds, we can assert that any change in the growth rate, all else the same, will increase the PV of CF. This is the profitable growth that investors look for.

In the second scenario, we have lowered the ROE where it is less than the cost of equity. Therefore, this translates into growth that is not profitable. This is why the PV of CF has decreased. If such a situation were to persist, then one of the ways to increase intrinsic value is to increase the dividend payout ratio.

In the third scenario, we have manipulated beta upwards and this has increased the cost of equity such that it is equal to ROE. In comparison to the first scenario where ROE>cost of equity, the intrinsic value has fallen.

In the last scenario we have indirectly manipulated the cost of equity such that ROE is slightly greater than cost of equity. In comparison to the third scenario, the intrinsic value has increased because of the relationship between these two variables. 

16.

In this example we are using the discounted cash flow method to determine the intrinsic value of a company and its stock. As we will see below, the primary change in the intrinsic values will be derived from the fact that the cost of equity and WACC are changing. The results are outlined in Exhibit B.  

If we assume the P/E multiple to be 16 in 2012, we derive intrinsic values of $37.61 for FCFF and $38.55 for FCFE (Exhibit A).  When compared to the benchmark, the intrinsic values are higher because investors are willing to pay more for each dollar of income than in 2011. The assumptions for this example are outlined in Exhibit A. 

When the unlevered beta is increased from 0.79 to 0.8 (scenario 2), the cost of equity and consequently the WACC increases. This intrinsic value is reduced as a result because investors demand a higher premium

Notably, in scenario 3, the market risk premium has increased by a full percentage point. This has served to increase the cost of equity from 11.7% to 12.6%. This also increases the WACC and as a result the cash flows are discounted by a higher figure and lower intrinsic values ensue.

The dividend discount model in comparison to the DCF model is more simplistic given the less number of variables required. However it can be argued the DCF model is more complete given its wholistic approach.

Exhibit A

Exhibit B

- Akhil P