Introduction

Generally speaking, investors tend to accept a greater level of investment volatility in exchange for higher expected returns. “ Hedge funds” and “diversified growth funds” offer investors the prospect of improved risk-adjusted returns by investing across a broad range of asset classes, and skilfully moving between them. A lot of these funds claim to be able to offer strong positive returns regardless of the market conditions.

One way to assess the performance of these sorts of funds is to carry out a multi-factor regression analysis against the key drivers of return (such as changes in the values of the asset classes available to invest in), to understand the extent to which:

•   their performance can be explained by the performance of the underlying assets

•   their reliance on different return factors may have changed overtime

In order to be able to generate positive returns regardless of market conditions,a fund would need to show evidence of strong historic returns which cannot be explained as a static combination of different asset classes. It would also ideally show relatively low volatility of returns.

The multi-factor regression model can be expressed as follows:

Ri,t  =  ri,t  +  wi, 1 f1,t  +  wi,2 f2,t  …  +  wi,nfn,t  + εi,t

Where

Ri,t  is thereturnover period t for hedge fund i.

ri,t  is the risk-free rate of return in period t.

wi,j  is an appropriate weight applied to the jth factor for the ith hedge fund.

fj,t  is the value of the jth factor in time period t. (for example the return of an underlying asset class) εi,t  is the error term,

This model has the advantage that no distributional assumption is needed about the returns of the assets.

The aim is to find the values of the weights for a given hedge fund which best explain the behaviour of the fund  in terms of the factors, or  in other words,  minimises  an  appropriate  measure  of the cumulative error terms. It is not always clear which factors or indeed how many factors to use when attempting to explain the behaviour of the fund.

One particular thing to consider is that the proposed model requires the assumption that the factors are independent. In financial markets this is unlikely to be the case, and can be investigated further. There area number of other assumptions underlying regression analysis which should be considered in the context of the data provided.

Available Resources

Data is available containing details of historical monthly Total Returns from a variety of asset classes between November 1998 and August 2023. You are also provided with monthly returns that a variety of hedge fund managers achieved over the same period.

Task

i.       Build a multi-factor regression model to explain the behaviour of the various hedge funds and comment on which funds appear to exhibit the most skill.

ii.       Present the results of the analysis and comment on the significance of the residuals and intercepts.

iii.      Consider the risk/return attributes of the various funds over different time periods – explain which funds you’d recommend a client invests in.

iv.       If you were looking to create a static fund (i.e. X% in asset class A, Y% in asset class B etc), what would be your allocation and why?

Possible extensions:

Should the impact of global events (e.g. Coronavirus outbreak) betaken into account when analysing datasets over the period?

UK gilt yields rose significantly during 2022, particularly in September 2022. How did the various hedge funds perform over this period? Can you explain this in terms of the factors in your model?

With the benefit of hindsight, and mean variance portfolio theory, comment on whether you think any of these funds have done what they said they could.

Consider whether having more data would help you come to a more informed conclusion.

Hints and tips

There is plenty of information about regression analysis for financial returns online, and how to apply this in Excel.

It should be noted that we have given the returns on UK fixed gilts and inflation-linked gilts, and on currency hedged and unhedged global equities. You should think about potential issues which might occur with  respect to linear independence / collinearity. Hint: can you isolate fixed gilt returns, inflation, equities, and currency as risk factors?

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