Statistical methods such as moving averages, Kalman filtering, exponential smoothing, regression analysis, and ARIMA (autoregressive integrated moving average) have been used for stock market predictions. However, these statistical methods have not produced superior performances. In recent years, machine learning techniques have been widely used in stock market predictions, including artificial neural network, SVM, and genetic algorithm. In particular, a case-based reasoning method, known as k-nearest neighbor is also widely used for stock price prediction. Case based reasoning retrieves several similar cases from previous cases when a new problem occurs, and combines the class labels of similar cases to create a classification for the new problem. However, case based reasoning has some problems. First, case based reasoning has a tendency to search for a fixed number of neighbors in the observation space and always selects the same number of neighbors rather than the best similar neighbors for the target case. So, case based reasoning may have to take into account more cases even when there are fewer cases applicable depending on the subject. Second, case based reasoning may select neighbors that are far away from the target case. Thus, case based reasoning does not guarantee an optimal pseudo-neighborhood for various target cases, and the predictability can be degraded due to a deviation from the desired similar neighbor. This paper examines how the size of learning data affects stock price predictability through k-nearest neighbor and compares the predictability of k-nearest neighbor with the random walk model according to the size of the learning data and the number of neighbors. In this study, Samsung electronics stock prices were predicted by dividing the learning dataset into two types. For the prediction of next day's closing price, we used four variables: opening value, daily high, daily low, and daily close. In the first experiment, data from January 1, 2000 to December 31, 2017 were used for the learning process. In the second experiment, data from January 1, 2015 to December 31, 2017 were used for the learning process. The test data is from January 1, 2018 to August 31, 2018 for both experiments. We compared the performance of k-NN with the random walk model using the two learning dataset. The mean absolute percentage error (MAPE) was 1.3497 for the random walk model and 1.3570 for the k-NN for the first experiment when the learning data was small. However, the mean absolute percentage error (MAPE) for the random walk model was 1.3497 and the k-NN was 1.2928 for the second experiment when the learning data was large. These results show that the prediction power when more learning data are used is higher than when less learning data are used. Also, this paper shows that k-NN generally produces a better predictive power than random walk model for larger learning datasets and does not when the learning dataset is relatively small. Future studies need to consider macroeconomic variables related to stock price forecasting including opening price, low price, high price, and closing price. Also, to produce better results, it is recommended that the k-nearest neighbor needs to find nearest neighbors using the second step filtering method considering fundamental economic variables as well as a sufficient amount of learning data.