###### 5 May 2016

## NZ Equity returns – future predictions

First up the headline here may be a bit misleading. It is common for many in this industry to predict the returns in the year ahead, and all we really know about predictions is that they will be wrong. Rather I am going to break down the components of return and allow you to make your own predictions.

The return to an equity index is often split up in terms of RE = RFR + ERP, where RFR = risk free rate (cash or bonds) and ERP = Equity Risk Premium (extra return for risk). The problem with this approach is that the ERP part can be difficult to estimate and arguably only works over very long time frames.

An approach I find intuitive is to split the equity return up into its component parts - income yield, earnings growth and repricing (the last two can be thought of together as capital gain). Any return you get must come from one of these three sources. This is known as the Grinold and Kroner model.

Expressed mathematically this gives the following equation:

ΔS = Change in shares (new issuance less buybacks)

D/P = Dividend yield

i = Inflation

g = Real earnings growth (not earnings per share)

ΔPE = Change in Price to Earnings ratio

The beauty of this approach is that you can then analyse each of these component parts in more detail. We will see that some of these terms are known, some can be reasonably estimated and some…..well best left to the reader.

Let us look through each of these in turn.

### Income yield

As at end of 2015 the net dividend yield of the NZX 50 was 4.66% so that’s pretty easy.

Stock issuance and buybacks are a relatively small component on the NZX market (as opposed to say US where buybacks are much more popular versus dividends). Looking back over 2015 we have had four buybacks in operation (Nuplex, Spark, Tower and Contact) the combined total of which appears to have been around $225m. Based on current NZX 50 market cap of around $70bn this is ~0.3%. There will also be a small amount of issuance every now and again so let’s say that is +0.1%. This gives us of -0.2% (negative as shares on issue is reducing). For different investors this could be deemed as capital gain or income but the effect is the same.

###

Earnings growth

Let’s look at inflation first. The chart from the reserve bank is below.

Source: RBNZ

Recent inflation has been low and we know the RBNZ targets a 1-3% range so let’s assume that targeting remains and over time we oscillate around the midpoint of 2%.

The next term, real earnings growth, is not so straightforward. A logical argument would dictate that real earnings growth should, over the long run at least, approximate real GDP growth. Otherwise it would result in corporate profits taking over the country or dwindling away. We can then further express it as follows:

Real Earnings growth ≅ Real GDP Growth = Labour force growth + Productivity

Labour force growth is shown in the graph below which shows the expected effects of moderating migration and ageing population reducing growth over time (though still marginally positive which is probably better than many other countries).

For the next decade using a figure of around 1% p.a. is around the mid point.

Productivity bounces around from year to year and tends to be measured in cycles, the current cycle from 2008 to 2015 has NZ productivity at 1.4% as per chart below:

Bring these together gives:

Real Earnings growth ≅ Real GDP Growth = Labour force growth + Productivity

Real Earnings growth ≅ 1% +1.4% = 2.4%

As somewhat of a sense check ANZ are currently “forecasting” real GDP growth of 2.8%, 2.5% and 2.6% over the next three years.

So to bring this all together, BEFORE we add the repricing element, you have the following:

Divivend Yield | 4.66% |

- Change in shares | -(-0.2%) |

+ Inflation | + 2.0% |

+ Real earnings Growth | + 2.4% |

= RETURN | 9.26% |

### Repricing

This brings us to the last term and repricing or change in P/E. This, as most investors know, can dominate equity returns in the short (and medium) term. Multiple components can contribute to changing PE ratios – inflation, discount rates etc. Though the hardest one to predict can be sentiment. Euphoria can push ratios unsustainably high and fear can drive them to unfeasible low numbers. The chart below (courtesy of Forsyth Barr) shows forward PE levels for the NZX market going back a few decades. As you can see the current level of 19 is over 6 points above the average for total period of 13.8x.

Rather than me predicting where the PE ratio will end up I will let the reader pick their own from the table below. You can pick the PE change and numbers of years for change to occur. The resultant value is your per annum expected return (the 9.26% return from above + the repricing element).

Do you think low interest rates and steady inflation justify lofty PE ratios? Or will the market return back to long term averages? Will it happen quickly (noting that reductions when they come in the chart above tend to be quite quick) or will it be a more gentle ride for investors?

The shaded red returns are less than current cash rate. Yellow is between cash and 7% (what could for many be the minimum return expected for taking equity risk?). Green is a return above 7% per annum.

Well, what colour are you?