Can both Bull and Bear show negative returns during the same period?

XACT Bulls investment objective is to return roughly one and a half times the return of the OMXS30 on a daily basis. Since the investment objective is very ease to grasp its easy to overlook what happens on day two. We would like to take this opportunity to discuss how the funds act over periods longer than one day.

Returns

To calculate returns we can use some simple maths.

If we invest 100 SEK in the index, the return will be

100*(1 + todays return) = Total return

Ex. 100 * (1 + 2 %) = 102 SEK

After our success during day one, we have more money in the market, 102 SEK. Assume that the index increases with another 2% also during the following day. We will then get a return on the profit from day one.

102*1,02=104,04 SEK

Or generally:

Investment * (1 + return) * (1 + return) etc..... (1+ return) = our total return at the end of the period

Ex. 100 SEK * (1 + 2%) * (1 + 2%)....(etc totalt 10 ggr) = 121,9 SEK

10 days with a 2 % daily return does not equal a 20 % return, it will yield a 21,9% return

The difference, 1.9%, is an effect of compounding returns which is the result of our initial investment has increased in value over several days. A return of 2% on a larger investment (102) will yield a higher return than on a smaller investment (100).

If you want to avoid this effect of interest on interest one should invest 100 on the market each day. Then you will get the final value of

100 + (100*return) + (100*return)...

Ex. 100 SEK + (100*2%)+(100*2%)... (etc 10 times) = 120 SEK

Leverage

What is leverage, as applied to Bull and Bear? Leverage means that when an investor invests 100 kr in the fund, the fund will borrow a further 50 SEK so that the investors exposure to the market is 150 SEK. Leverage is very good if the market goes your way, but it will hurt when the market goes against you.

Leverage amplifies both upwards and downwards movements. We use a daily change of +10% and -10% to really emphasise the effect in the index.

(a) Index:                                                  100*(1+10%)*(1-10%) = 99

(b) Bull or Bear:                                       100*(1+15%)*(1-15%) = 97,75

(c) or with two times leverage:                 100*(1+20%)*(1-20%) = 96

Are the funds worth the same amount each time the index reaches a prevous level?

No, neither Bull nor Bear will be worth the same when index returns to a previous level. As we saw above, the index needs a bigger percentage upward movement than downward movement to avoid losing in value. If we construct an example where the daily return is +10% and  -9,0909% the index will return to the same level as before. This is an extreme example, and 10% daily movements are on par with the index biggest movements ever, just to create a big effect. In real life the effects are much less.

We can observe the following:

Do the losses from volatility mean that Bull and Bear will never return more than index? No, on the contrary, if the market has moved your way it is very likely that the product that you invested in will have an accelerated return, especially over shorter time periods. But it does mean that the returns depend on the path the funds take from one index level to another. When index is back at its starting value, the funds value will always be less.

The advantages of leverage

So is leverage always bad in the long term? No, not at all. As long as the market does not change direction from plus till minus the interest on interest effect will benefit a leveraged fond compared to a non-leveraged fund.

(d) Index:                                                  100*(1+10%)*(1+10%)=121

(e) Bull:                                                     100*(1+15%)*(1+15%)=132.25

(f) or with two times leverage:                 100*(1+20%)*(1+20%)=144

In scenario (d) index has returned 21% whilst Bull has returned 32.35% which is 1% percentage point better than one and a half times the index. This is thanks to the compounding of returns that is to our benefit in this trending market.

In times with a down trending market, it is not as bad to have leverage as one might think at first.

(g) Index:                                                 100*(1-10%)*(1-10%)=81

(h) Bull:                                                    100*(1-15%)*(1-15%)=72.25

(i) or with two times leverage:                 100*(1-20%)*(1-20%)=64

Undenaiably you will lose a lot of money in scenario (h), but will you loose more than one and a half times the index return? No, actually not. In scenarion (g) the index has returned -19%. Bull has returned 27.75% which is 0,75% better than one and a half times the index
(-28,5%). This is due to the compounding effect which is working to the benefit of our investment, also in this case. A conclusion one can make is that if a market has a clear trend, be it up or down, it will be beneficial to own leveraged funds. But, it is crucial to choose the right one.

Conclusions

• - The funds will take different values, that will be lower and lower each time index returns to its initial level.
• - During one day equal investments in Bull and Bear will return the same
• - Each day can be viewed as a new day, with a new investment
• - The effect of Interest on interest is negative in periods of high volatility
• - If you think that the market will increase buy Bull. If you think the market is going to decrease buy Bear. If you would like to lose less on volatility buy XACT OMXS30.