Chapter 2: Financial Markets: Part 2
Portfolio Allocation and the demand for assets
There are three main determinants of asset pricing:
1) Expected return: The higher the expected return of the asset, all else constant, the higher the price of the asset. Naturally, we will discuss at length the factors that influence the expected return of the asset(s) throughout the course. I do want to mention at this point how important expectations and changes in expectations are in terms of determining not only asset prices, but also, aggregate economic activity.
Asset price = f (Rete) :
+
{stated as “the asset price is a positive (+) function (f) of it’s expected return (Rete), all else constant}
2) Liquidity: Liquidity is an attractive quality in any asset and a highly liquid asset has three qualities: 1) it is easy (low cost) to convert the asset into money where money is defined as transactions money; 2) it can be converted to money quickly and 3) the amount that it is converted to is representative of its fundamental value (i.e., I can sell my house very quickly and easily for $5, but that doesn’t mean it is liquid!). Typically, the more liquid the asset, the lower the return. Take money, typically considered to be the most liquid asset of all. Money earns a nominal return of zero and a real return equal to the ‘negative’ of the inflation rate.[1]
Liquidity is especially attractive in a highly uncertain environment. When we discuss financial crises and shocks like 9/11, we will see the impact on financial markets when investors demand more liquid assets. US Treasuries are often considered very liquid and thus the term: “rush to the safe haven of US Treasuries.” The safe haven refers naturally to the perceived zero default risk quality of US Treasuries.
Asset price = f (Liq) :
+
{stated as “the asset price is a positive (+) function (f) of it’s liquidity (Liq), all else constant}
3) Risk: The more risky the asset, the more uncertain as to the assets’ return. Risk arises for a variety of reasons and we assume that all else equal, investors prefer assets with less risk (i.e., on average, investors are risk averse). We also note that risk and expected return are related – typically, the higher the risk, the higher the expected return (investors require a higher expected return to take on the higher risk).
Asset price = f (Risk) :
-
{stated as “the asset price is a negative (-) function (f) of it’s Risk, all else constant}
Stock Price Determination
As most of us could gather, the obvious driving force underlying any the price of any stock is the expected future stream of profits or earnings (earnings and profits are used interchangeably). We need to be more specific, it is the present value (PV) of current and future earnings that matter. We all should recall that the present value of say $1,000 today is larger than the present value of $1,000 ten years from now. But how much larger? The answer depends on the expected nominal interest rate to prevail over the next ten years. Let’s make life simple, let us suppose that the interest rate over the next ten years will be 10% year in and year out. In this case, given these assumptions, the PV of $1,000 ten years from now would be:
PV1000 = $1,000/(1 + 0.10)10 = $ 385.54
What does $385.54 represent? The answer is that if we take $385.54 and invest it today at a 10% annual return and take the principal and interest and continue rolling it over for 10 years, at the end of the 10th year, we would have $1,000. An equivalent way of thinking about this is, and the way most relevant for understanding how stock prices are determined is the following: Given the above conditions, I would be willing to pay $385.54 today, to receive $1,000 ten years from now. In what follows, the $1,000 in this example would be the “expected profits” of the firm ten years from now. These expected profits are continuously changing given the continuous NEWS that investors digest and process on a day to day basis.
In terms of stock price determination, investors form expectations as to the future profits of any particular firm as well as the expected path of interest rates, since together, they determine the present value of the firm. Similar to the above, the present value of a firm can be thought of as the most investors would be willing to pay for the firm today, to have the ownership rights to all the current and future profits expected in the future. When we divide the present value of the firm by the number of shares of stock outstanding, we arrive at the price of the stock. Before getting into more specifics, please read the following summation.
Three major factors to keep in mind when considering stock price determination
1) Stock prices are driven by expectations and changes in expectations. Just about everything influences expectations and these changes in expectations are reflected immediately in the relevant stock price.[2]
2) Stock prices are positively related to expected earnings and expected earnings nearer to the present have a stronger influence on stock prices than do the same expected earnings further out into the future. For example, the present value of $10,000 in expected earnings 2 years from now is larger than the present value of $10,000 in expected earnings 10 years from now (assuming away zero interest rates)[3]
3) Stock Prices are typically negatively related to the expected path of interest rates. The expected path of interest rates is so important in financial markets, not to mention, aggregate economic activity. Many investors spend much of their time trying to figure out what the Federal Reserve may or may not do. Interest rates also change for reasons not directly related to Fed policy, and a big portion of this class revolves around interest rate determination. For the present, we need to understand why lower interest rates are ‘typically’ good for stocks. First, the present value of future profits rises the lower the expected path of interest rates. Let’s return to our example above. It was shown that the PV of $1,000 ten years from now, assuming 10% interest rates year in and year out, was:
PV1000 = $1,000/(1 + 0.10)10 = $ 385.54
Now let’s let the expected path of interest rates be 5% year in and year out. What is the PV of $1,000 ten years from now given this lower expected path of interest rates?
PV1000 = $1,000/(1 + 0.05)10 = $ 613.91
So if the expected path of interest rates fall, all else constant, that should be good for stocks as the PV of the firm will rise.
Second, we can not ignore the influence of the change in the expected path of interest rates on expected profits. This influence is very real but also very hard to analyze and therefore, the context must be taken into account. For example, on one hand, lower interest rates in the future should stimulate economic activity and according to this version of the story, should result in higher expected profits. On the other hand, if people expect lower interest rates due to a poorly performing economy, then perhaps expected profits will fall instead of rise. So the influence of lower expected interest rates on the expectations of future profits is ambiguous, and thus, needs to be examined on a case by case basis.
Numerical Example and some Terminology
The stock price of any firm is equal to the (expected) present value of the firm (market cap) divided by the number of shares outstanding. Any factor, and there are many, that changes the expected present value of the firm, will change that stock price.[4]
The assumption (in the numerical example that follows) is that this firm falls off the face of the earth after three years, a more realistic example would include many more terms (an infinite amount!).
Example:
Company ABC (10,000 shares outstanding)Year / 1 / 2 / 3
Exp. Earnings / $15,000 / $50,000 / $100,000
Exp. 1 yr Interest Rate / 0.03 / 0.04 / 0.05
Price to earnings ratio (PE ratio): The price to earnings ratio is often used by investors as a guidepost as to whether a stock is “overvalued” or “undervalued.” Given that stock prices are determined by expectations of the future, we NEVER know whether a stock price is overvalued, undervalued, or valued ‘just right.’[5]
The price to earning ratio can be calculated in two equivalent ways:
1) Take the market cap, which is equal to the number of shares outstanding times the current price of the stock and divide it by current year earnings. From the example above:
PE ratio = $147,175 / $15,000 = 9.81
2) Take the price per share and divide it by current year earnings per share:
PE ratio = $14.72 / $1.50 = 9.81
We can now do some exercises:
1) Suppose the Federal Reserve makes a dovish announcement and as a result, investors expect the path of short term interest rates to be steady at 3% (as opposed to previous expectations over the three year life of the firm of 3, 4, and 5% respectively).
Exercise: What will happen to the Stock Price?[6]
Exercise: What will happen to the PE ratio?
2) Suppose the CEO of Company ABC makes a statement that the company’s expected earnings are now lower than previously expected (i.e., a pessimistic outlook) so that investors now expect profits to be ‘flat’ at $15,000 for the next three years (assume the initial expected path of interest rates of 3, 4, and 5% in year 1, 2, and 3 respectively).
Exercise: What will happen to the Stock Price?
Exercise: What will happen to the PE ratio?
3) Give two specific reasons why the PE ratio would be high for a firm and comment on the type of firm that may have a high PE ratio. Finally, does a high PE ratio imply that the firm is over valued? Why or why not?
The Optimal Forecast and Rational Expectations.
Example 1: Rational Expectations and a Question Before You Hand in Your Exam!
When I was at Grad School here at PSU, a professor told a story that I believe really clarifies exactly what we mean by rational expectations. Suppose I would say to the class before anyone handed in their exam (assume it is a multiple choice exam):
“Put an asterisk next to the three questions that you think you missed”
So let’s think about this for a moment……. which questions would you pick? The answer is that if you have rational expectations formation, you should not pick any! Why?? If you pick a question that you think you missed, then change the answer! Of course I know a lot of you are thinking that well…. some questions are harder than others and I will simply choose the three hardest questions! That is fine and consistent with rational expectations, but that is not admitting that you think you missed them because if you think you missed it, again, you would change the answer. So again, if I asked you how many questions you think you missed, your answer should be zero!
Another interesting and useful feature of this example is the concept of a probability distribution – some questions probably fall into the ‘no brainer’ category and thus, you are quite certain that you got them correct; some are in the easy but not that easy, etc. As we shall see, probability distributions and the associated uncertainty plays a critical role in financial markets and the economy.
Example 2: Using Rational Expectations on Your Drive to Work Each Day
Suppose you live in Port Matilda and work in State College. Suppose also that you do not want to arrive at work “too” early and you don’t want to arrive at work “too” late. Suppose through experience, you estimate the commute to be 15 minutes and thus leave 15 minutes before you are scheduled to work.[7] Suppose you begin work at 8 am and thus you leave at 7:45 am.
Questions:
1) Would you expect to get to work at starting time each and everyday?
2) Would you actually get to work at exactly the same time?
3) Is your forecast of the time it takes to get to work optimal? Why or why not?
Consider the following two scenarios:
a) One the way to work you get stuck in traffic due to an accident, somebody hit a deer and you end up getting to work 15 minutes late!
Question: Would you change your forecast on how long it takes to get to work and would this forecast be optimal?
b) The state begins construction (on the road you travel) and you are 15 minutes late for work. You learn that the construction is going to last for 6 months. Would you change your forecast on how long it takes to get to work and would this forecast be optimal?
Let’s define the forecast error (FE) as the starting time (8 am) minus (-) the actual arrival time. If the actual arrival time is 8am, then the forecast error equals zero; if the arrival time is not 8 am, then the FE is non-zero. What are the properties of this forecast error (there are three of them)?
a.
b.
c.
Predicting Tomorrow’s Stock Price and the Efficient Market Theory
In the driving to work example above, we had the incentive to obtain an optimal forecast for the commute and thus, we used all the relevant information available to formulate that optimal forecast. For example, if it snowed all night and you believed the roads are likely to be slippery, you would use that relevant and available information immediately and incorporate (process the information) it into your forecast of the time it will take to get to work. In terms of jargon, we would say you were irrational if you did not account for the snowfall.