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Richard R. Lindsey & Andrew B. Weisman

Q Group

October, 18, 2015

This presentation is for information purposes only and should not be used or construed as an offer to sell, a solicitation of an offer to buy, or a recommendation for any security. There is no guarantee that the information supplied is accurate, complete, or timely, nor do es it make any warranties with regards to the results obtained from its use. It is not intended to indicate or imply in any manner that curr ent or past results are indicative of future profitability or expectations. As with all investments, there are inherent risks that individuals would need to consider .

The views expressed are those of the speaker and do not necessarily reflect the views of others in the Janus organization.

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There was an (almost) magical hedge fund with high returns and low volatility…

But subprime mortgage delinquencies grew, and the value of securities held by the fund dropped…

The Prime Brokers for the fund asked for more cash collateral…

The fund tried to liquidate assets in a declining market to meet the collateral calls…

But asset values continued to decline quickly while collateral requirements continued to rise…

The fund failed even though its parent company attempted to stabilize it with a substantial cash injection…

Investors were returned 9^{â‚µ} on the dollar…

And the managers lived happily ever after…

Typical approach is to diversify across securities and strategies,

using the common “currencies”

Return

Volatility

Correlation

Consequences

Looking for low correlation and low volatility

Low volatility and correlation often an “accounting artifact”

Drawn to securities with limited price discovery

Investors tend to believe in a “liquidity premium” that compensates them for illiquidity

Lo, et al (2003)

Add liquidity as additional constraint in mean-variance optimization

Seigel (2008); Leibowitz & Bova (2009)

Consider liquidity in determining portfolio weights

Ang, et al (2011)

Optimal liquidity policy with market frictions

Kinlaw, et al (2013)

Liquidity as a shadow allocation in the portfolio

Illiquid portfolios tend to exhibit a high degree of positive serial correlation (Weisman (2003); Getmansky et al (2004))

Methods:Scholes & Williams (1977); Geltner (1993); Getmansky, et al (2004); Bollen & Poole (2008); Anson (2010); Anson (2013)

Adjust the time series for serial correlation Decode the performance to adjust volatility and correlations

Primary Question:Are under-reported volatility and correlation a benign consequence of illiquidity or is there more to it?

What should concern you most as an investor?

We argue that simply adjusting for serial correlation fails to measure or capture the core risk and cost of illiquidity that investors should care about: forced liquidations and “fire sales”

**A mismatch between the funding of an underlying investment and the horizon over which the investment can be sold**

**Leverage/Financing**:(Garleanu& Pedersen (2009); Brunermeier & Pedersen (2009); Office of Financial Research (2013))

–Including swaps, futures, margin

** Contractual terms:** (Ang & Bollen(2010))

–Gates, lock ups, notice periods

**Network factors **:(Battacharya, et al (2013); Gennaioli, et al (2012); Boyson, et al (2010); Mitchell, et al (2007); Chen, et al (2012); Schmidt, et al (2013))

–Common service providers (custodians, prime brokers, securities lending counterparties)

–Unanticipated strategy correlation

–Common investors

The true value of the portfolio assumed to follow a discrete Brownian motion:

Bayesian process of adjusting some proportion of the distance between prior period’s valuation and what it’s perceived to be worth in the current period (Quanand Quigley (1991))

The observed (reported) return is a function of:

–The trend rate of return

–The realized volatility

–The under/over-valuation of the prior period

(Not the only method for deriving this prior: common sense “sanity checks” also useful…)

How are N_{t} (true value) and R_{t}(reported value) related?

**Illiquidity systematically drives under/over-valuation**

**Under-valuation not so critical, over-valuation more of an issue:**

Interested third parties will not allow a portfolio valuation to exceed a rational tradable value by more than a “reasonable” margin

Prime brokers that extend credit, monitor reported valuations as assets serve as collateral

We refer to this margin as the “credibility threshold” (L)

L effectively determined by the first interested third party such as Prime Brokers or investors to act;

NOT THE MANAGER

Exceeding the credibility threshold triggers forced behavior (selling)

May result in a large single period loss governed by:

The portfolio overvaluation (R_{t}-N_{t})

A liquidation penalty (P)

Such losses relatively frequent and tend to be larger than conventional data-dependent methods such as VaR or CVaR

The magnitude and frequency (not the timing) are reasonably predictable, and can be pricedby formalizing the basic structural dynamics

Simulate the “true” value of portfolio using discrete BM which is a function of:

Simulate 100k times and calculate the mean NPV of all the one-year paths (including those which do not cause liquidation)

This naturally translates into a “haircut” against the observed return and represents a de facto price for investing in a less liquid portfolio

The option value is not a liquidity premium, rather it is the calculated cost of price smoothing an illiquid portfolio when combined with a triggering event, that may result in an abrupt sale into a declining market

When the portfolio is illiquid, managers generally do not have the flexibility to avoid these dynamics

In cases of fraud or collapse, transactions in the secondary market for hedge funds have an average discount to NAV

of 49.6% (Ramadorai(2008))

**JPMorgan (2012)**

Hedge funds expected return 5% to 7%

Hedge funds expected volatility 7% to 13%

Private equity expected returns 9%

Private equity expected volatility 34.25%

Are these sufficient returns given the volatility?

Measured serial correlation for most of these lie in the 50% to 60% range

Managers are typically reflecting less than 50% of the true change in the value of their portfolios

Depending on assumptions concerning other parameters, the option value could be quite significant!

Example: Emerging Market liquidity option: 13.52%Observed return: 17.3%, Liquidity-adjusted return: 3.78%

Morningstar-CISDM Hedge Fund Database (contains both live and dead funds)

Eliminated CTAs and Fund of Funds

At least 24 months of return history

Autocorrelation of 0.01 or higher

Eliminate the last 3 months of data for each manager

**3,554 hedge funds**

Average Option value was 5.52%Implying an average Liquidity-adjusted mean return of 6.27%

The (almost) magical fund: Bear Stearns High-Grade Structured Credit Strategies

µ=12.4% Ïƒ=1.5% Î»=0.3635

Option value close to $0, but…

The standard deviation for the HFRI Fixed Income–Asset Backed Index: 4.03%

The Bear Stearns Fund was showing â‰ˆ 1/3 of the index volatility

As the fund’s volatility approached the index volatility, the option cost exploded

Adjusting for serial correlation fails to measure or capture the core risk and cost of illiquidity: forced liquidations and “fire sales”

A barrier option model provides a straight-forward method of combining priors about the market to price this core risk